%!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: WS0001Ub6V2.dvi %%Pages: 2 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips WS0001Ub6V2.dvi %DVIPSParameters: dpi=300, compressed, comments removed %DVIPSSource: TeX output 2000.11.28:0946 %%BeginProcSet: texc.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{ /nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{ /sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0] N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{ 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 sub]/id ch-image N /rw ch-width 7 add 8 idiv string N /rc 0 N /gp 0 N /cp 0 N{rc 0 ne{rc 1 sub /rc X rw}{G}ifelse}imagemask restore}B /G{{id gp get /gp gp 1 add N dup 18 mod S 18 idiv pl S get exec}loop}B /adv{cp add /cp X}B /chg{rw cp id gp 4 index getinterval putinterval dup gp add /gp X adv}B /nd{/cp 0 N rw exit}B /lsh{rw cp 2 copy get dup 0 eq{pop 1}{ dup 255 eq{pop 254}{dup dup add 255 and S 1 and or}ifelse}ifelse put 1 adv}B /rsh{rw cp 2 copy get dup 0 eq{pop 128}{dup 255 eq{pop 127}{dup 2 idiv S 128 and or}ifelse}ifelse put 1 adv}B /clr{rw cp 2 index string putinterval adv}B /set{rw cp fillstr 0 4 index getinterval putinterval adv}B /fillstr 18 string 0 1 17{2 copy 255 put pop}for N /pl[{adv 1 chg} {adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{ adv rsh nd}{1 add adv}{/rc X nd}{1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]dup{bind pop}forall N /D{/cc X dup type /stringtype ne{] }if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{ cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict /eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false} ifelse}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail {dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M} B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{ 4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{ p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end %%EndProcSet TeXDict begin 39158280 55380996 1000 300 300 (WS0001Ub6V2.dvi) @start /Fa 1 83 df82 D E /Fb 3 52 df<1206120E12FE120EB1EAFFE00B157D9412>49 DII E /Fc 1 1 df0 D E /Fd 4 104 df71 D<38FFC0FF381C00181410A3481320A44813 40A4481380A4EB010013025BEA6008EA3830EA0FC018177E9618>85 D97 D<13E2EA031EEA060E120C130C1218A3EA1018A3EA1838EA08F0EA07301200A2EA60 6012E0EAC1C0EA7F000F14808D11>103 D E /Fe 8 107 df0 D<90380FFFFC137FD801F0C7FCEA03800006C8FC5A5A5AA25AA25AA81260A27EA27E7E7E 6C7EEA01E039007FFFFC131F1E1E7C9A27>26 D<4B7EA46F7EA2166082A2161C8282B812 E0A2C9EA0700160E5E1630A25E5EA24B5AA42B1A7D9832>33 D50 D<12C0A812E0A212C0A803127D9400>55 D102 D<12F8120FEA03806C7E6C7EB113707F131EEB03C0EB1E00 13385B5BB1485A485A000FC7FC12F812317DA419>I<12C0B3B3AD02317AA40E>106 D E /Ff 13 121 df<127012F812FCA212741204A41208A21210A212201240060F7C840E >59 D<90B6128090380F00071501A2131EA21600A25BA2140192C7FCEB7802A21406140E EBFFFCEBF00CA33801E008A391C8FC485AA4485AA4120FEAFFFC21227DA120>70 D<027F1340903903C0C08090380E00214913130170130F49EB0700485A485A48C7FC4814 02120E121E5A5D4891C7FCA35AA4EC3FFF48EB00F0A34A5A7EA212704A5A7E001813076C 13096CEB1180380380E0D8007FC8FC22247DA226>I<9039FFF801FF010FC71278166016 C0011EEB010015025D5D4913205D5D0202C7FC495A5C141C147CEBF0BEEBF11E13F2EBF8 0FEA01F001E07F1407A248486C7EA36E7EEA0780811400A2000F497E39FFF80FFF28227D A129>75 DI<9039FF8007FE010FEB00F0 16C0D90BC0134001131480A2EB11E0A2903921F001001320A2147801401302147C143CA2 496C5AA3140FD801005B15881407A20002EB03D0A215F01401485C1400A2120C001E1440 EAFFC027227DA127>78 D86 D97 D<141EEC638014C71301ECC30014801303A449C7FCA4EBFFF8010EC7FCA65BA55BA55BA4 136013E0A25BA21271EAF18090C8FC1262123C192D7EA218>102 DI<13F0EA07E01200A3485AA4485AA448C7FCEB0F80EB30C0EB4060380E8070EA 0F00120EA24813E0A4383801C0A2EB0380148200701384EB07041408130300E013103860 01E017237EA21C>I<383C07C038461860384720303887403813801300A2000E1370A448 13E0A2EB01C014C1003813C2EB03821484130100701388383000F018157E941D>110 D<3801E0F03806310C38081A1C0010133CEA201C14181400C65AA45BA314083860E01012 F0142038E1704038423080383C1F0016157E941C>120 D E /Fg 57 128 df<137CEA018738030380000713C0EA0601000E13E0A514C0EB0380A2EB0E00EA FE38EA0E06EB0380EB01C0A2EB00E014F0A214701478A61470A2EB70E014C0EB718038FE 1F0015237FA218>25 D<132013401380EA01005A12061204120CA25AA25AA312701260A3 12E0AE1260A312701230A37EA27EA2120412067E7EEA0080134013200B327CA413>40 D<7E12407E7E12187E12041206A27EA2EA0180A313C01200A313E0AE13C0A312011380A3 EA0300A21206A21204120C5A12105A5A5A0B327DA413>I<127012F812FCA212741204A4 1208A21210A212201240060F7C840E>44 DI<127012F8A31270 05057C840E>I48 D<13801203120F12F31203B3A9EA07C0EAFFFE0F217CA018>III<1303A25BA25B1317A213271367134713871201 13071202120612041208A212101220A2124012C0B512F838000700A7EB0F80EB7FF01521 7FA018>I<00101380381E0700EA1FFF5B13F8EA17E00010C7FCA6EA11F8EA120CEA1C07 381803801210380001C0A214E0A4127012F0A200E013C01280EA4003148038200700EA10 06EA0C1CEA03F013227EA018>I<137EEA01C138030080380601C0EA0C03121C38180180 0038C7FCA212781270A2EAF0F8EAF30CEAF4067F00F81380EB01C012F014E0A51270A300 3813C0A238180380001C1300EA0C06EA070CEA01F013227EA018>I<127012F8A3127012 00AB127012F8A3127005157C940E>58 D61 D<497EA3497EA3EB05E0A2EB09F01308A2EB1078A3497EA3497EA2EBC01F497EA248B512 80EB0007A20002EB03C0A348EB01E0A348EB00F0121C003EEB01F839FF800FFF20237EA2 25>65 DI<903807E0109038381830EBE0063901C0017039038000F0 48C7FC000E1470121E001C1430123CA2007C14101278A200F81400A812781510127C123C A2001C1420121E000E14407E6C6C13803901C001003800E002EB381CEB07E01C247DA223 >IIII<903807F00890383C0C18EBE0023901C001B839038000F848C7 1278481438121E15185AA2007C14081278A200F81400A7EC1FFF0078EB00F81578127C12 3CA27EA27E7E6C6C13B86C7E3900E0031890383C0C08903807F00020247DA226>I<39FF FC3FFF390FC003F039078001E0AE90B5FCEB8001AF390FC003F039FFFC3FFF20227EA125 >II75 DII<39FF8007FF3907C000F81570D805E01320EA04F0A21378 137C133C7F131F7FEB0780A2EB03C0EB01E0A2EB00F014F81478143C143E141E140FA2EC 07A0EC03E0A21401A21400000E1460121FD8FFE0132020227EA125>I82 D<3803F020380C0C60EA1802383001E0EA70000060136012E0A21420A36C1300A2127812 7FEA3FF0EA1FFE6C7E0003138038003FC0EB07E01301EB00F0A214707EA46C1360A26C13 C07E38C8018038C60700EA81FC14247DA21B>I<39FFFC07FF390FC000F86C4813701520 B3A5000314407FA2000114806C7E9038600100EB3006EB1C08EB03F020237EA125>85 D<387FFFFE387E003E0078133C007013781260004013F012C0EB01E0388003C0A2EB0780 1200EB0F005B131E5BA25BA25B1201EBE001EA03C0A2EA07801403EA0F00001E1302A248 1306140E48131E00F8137EB512FE18227DA11E>90 D97 D<120E12FE121E120EAB131FEB61C0EB8060380F0030000E1338143C141C 141EA7141C143C1438000F1370380C8060EB41C038083F0017237FA21B>II<14E0130F13011300ABEA01F8EA0704EA0C02EA1C01EA3800 1278127012F0A7127012781238EA1801EA0C0238070CF03801F0FE17237EA21B>II<133E13E33801C780EA0387130748 C7FCA9EAFFF80007C7FCB27FEA7FF0112380A20F>I<14703803F198380E1E18EA1C0E38 380700A200781380A400381300A2EA1C0EEA1E1CEA33F00020C7FCA212301238EA3FFE38 1FFFC06C13E0383000F0481330481318A400601330A2003813E0380E03803803FE001521 7F9518>I<120E12FE121E120EABEB1F80EB60C0EB80E0380F0070A2120EAF38FFE7FF18 237FA21B>I<121C123EA3121CC7FCA8120E127E121E120EB1EAFFC00A227FA10E>I<13E0 EA01F0A3EA00E01300A81370EA07F012001370B3A51260EAF0E013C0EA6180EA3F000C2C 83A10F>I<120E12FE121E120EABEB03FCEB01F014C01480EB02005B5B5B133813F8EA0F 1CEA0E1E130E7F1480EB03C0130114E0EB00F014F838FFE3FE17237FA21A>I<120E12FE 121E120EB3ADEAFFE00B237FA20E>I<390E1FC07F3AFE60E183803A1E807201C03A0F00 3C00E0A2000E1338AF3AFFE3FF8FFE27157F942A>I<380E1F8038FE60C0381E80E0380F 0070A2120EAF38FFE7FF18157F941B>III114 DI<1202A41206A3120E121E123EEAFFFCEA0E00AB1304A6EA07 081203EA01F00E1F7F9E13>I<000E137038FE07F0EA1E00000E1370AD14F0A238060170 380382783800FC7F18157F941B>I<38FF80FE381E00781430000E1320A26C1340A2EB80 C000031380A23801C100A2EA00E2A31374A21338A3131017157F941A>I<39FF8FF87F39 3E01E03C001CEBC01814E0000E1410EB0260147000071420EB04301438D803841340EB88 18141CD801C81380EBD00C140E3900F00F00497EA2EB6006EB400220157F9423>I<38FF 80FE381E00781430000E1320A26C1340A2EB80C000031380A23801C100A2EA00E2A31374 A21338A31310A25BA35B12F05B12F10043C7FC123C171F7F941A>121 D<383FFFC038380380EA300700201300EA600EEA401C133C1338C65A5B12015B38038040 EA07005A000E13C04813805AEA7801EA7007B5FC12157F9416>I127 D E /Fh 21 122 df65 D<91387FE003903907FFFC07011FEBFF0F90397FF00F9F9039FF00 01FFD801FC7F484880484880484880485A82485A82127FA290CAFC5AA892B512F87E7F03 001300123FA26C7EA26C7E6C7E6C7E6C7E6CB45B90387FF007011FB5129F0107EBFE0F90 39007FF0032D297CA835>71 D73 D76 D<3803FF80000F13F0381F01FC383F80FE147F801580EA1F00C7 FCA4EB3FFF3801FC3FEA0FE0EA1F80EA3F00127E5AA4145F007E13DF393F839FFC381FFE 0F3803FC031E1B7E9A21>97 DIIII<9038FF80F00003EBE3F8 390FC1FE1C391F007C7C48137E003EEB3E10007EEB3F00A6003E133E003F137E6C137C38 0FC1F8380BFFE00018138090C8FC1238A2123C383FFFF814FF6C14C06C14E06C14F0121F 383C0007007CEB01F8481300A4007CEB01F0A2003FEB07E0390FC01F806CB5120038007F F01E287E9A22>103 DI<1207EA0F80EA1FC0EA3FE0A3EA 1FC0EA0F80EA0700C7FCA7EAFFE0A3120FB3A3EAFFFEA30F2B7EAA12>I108 D<26FFC07FEB1FC0903AC1FFC07FF0903AC307E0C1F8 D80FC49038F101FC9039C803F20001D801FE7F01D05BA201E05BB03CFFFE3FFF8FFFE0A3 331B7D9A38>I<38FFC07E9038C1FF809038C30FC0D80FC413E0EBC80701D813F013D0A2 13E0B039FFFE3FFFA3201B7D9A25>II<38FFC1F0EBC7FCEBC63E380FCC7F 13D813D0A2EBF03EEBE000B0B5FCA3181B7F9A1B>114 D<3803FE30380FFFF0EA3E03EA 7800127000F01370A27E00FE1300EAFFE06CB4FC14C06C13E06C13F0000713F8C6FCEB07 FC130000E0137C143C7E14387E6C137038FF01E038E7FFC000C11300161B7E9A1B>I<13 E0A41201A31203A21207120F381FFFE0B5FCA2380FE000AD1470A73807F0E0000313C038 01FF8038007F0014267FA51A>I<39FFE07FF0A3000F1307B2140FA2000713173903F067 FF3801FFC738007F87201B7D9A25>I<39FFFC03FFA3390FF000F0000714E07F0003EB01 C0A2EBFC0300011480EBFE070000140013FFEB7F0EA2149EEB3F9C14FC6D5AA26D5AA36D 5AA26D5AA25CA21307003890C7FCEA7C0FEAFE0E131E131C5BEA74F0EA3FE0EA0F802027 7F9A23>121 D E /Fi 32 128 df<1238127C12FEA3127C123807077C8610>46 D<14181438A21470A214E0A3EB01C0A2EB0380A3EB0700A3130EA25BA35BA25BA35BA248 5AA3485AA248C7FCA3120EA35AA25AA35AA25AA25A15317DA41C>I<13FE3807FFC0380F 83E0381F01F0383E00F8A248137CA312FC147EAD007C137CA36C13F8A2381F01F0380F83 E03807FFC03800FE0017207E9F1C>I<13181378EA01F812FFA21201B3A7387FFFE0A213 207C9F1C>II54 D66 D68 D73 D77 D80 D<3801FE023807FF8638 1F01FE383C007E007C131E0078130EA200F81306A27E1400B4FC13E06CB4FC14C06C13F0 6C13F86C13FC000313FEEA003F1303EB007F143FA200C0131FA36C131EA26C133C12FCB4 13F838C7FFE00080138018227DA11F>83 D85 D87 D97 D99 DI<13FE3807FF80380F87C0381E01E0003E13F0EA 7C0014F812FCA2B5FCA200FCC7FCA3127CA2127E003E13186C1330380FC0703803FFC0C6 130015167E951A>II<3801FE0F3907FFBF80380F87C7381F03E7391E01 E000003E7FA5001E5BEA1F03380F87C0EBFF80D809FEC7FC0018C8FCA2121C381FFFE06C 13F86C13FE001F7F383C003F48EB0F80481307A40078EB0F006C131E001F137C6CB45A00 0113C019217F951C>II<121C123E127FA3123E121CC7FCA7B4FCA2121FB2EAFFE0A2 0B247EA310>I108 D<3AFF07F007F090391FFC 1FFC3A1F303E303E01401340496C487EA201001300AE3BFFE0FFE0FFE0A22B167E9530> I<38FF07E0EB1FF8381F307CEB403CEB803EA21300AE39FFE1FFC0A21A167E951F>I<13 FE3807FFC0380F83E0381E00F0003E13F848137CA300FC137EA7007C137CA26C13F8381F 01F0380F83E03807FFC03800FE0017167E951C>I114 DI<487EA41203A21207A2120F123FB5FCA2EA0F80AB EB8180A5EB8300EA07C3EA03FEEA00F811207F9F16>I<38FF01FEA2381F003EAF147E14 FE380F81BE3907FF3FC0EA01FC1A167E951F>I<39FFE01FE0A2391F800700000F1306EB C00E0007130C13E000035BA26C6C5AA26C6C5AA2EB7CC0A2137F6D5AA26DC7FCA2130EA2 1B167F951E>I127 D E end %%EndProlog %%BeginSetup %%Feature: *Resolution 300dpi TeXDict begin %%PaperSize: a4 %%EndSetup %%Page: 1 1 1 0 bop 162 274 a Fi(Mathematisc)n(hes)17 b(Institut)659 b(WS)19 b(2000/2001)162 334 y(der)f(Univ)n(ersit)487 336 y(\177)487 334 y(at)g(M)609 336 y(\177)607 334 y(unc)n(hen)828 b(Blatt)18 b(6)162 394 y(Prof.)g(Dr.)h(B.)f(P)n(areigis)307 691 y Fh(Lineare)23 b(Algebra)g(und)g(analytisc)n(he)h(Geometrie)e(I) 197 790 y Fg(21.)j(Sei)15 b Ff(G)i Fg(eine)e(Grupp)q(e.)i(F)742 792 y(\177)741 790 y(ur)f Ff(g)g Fe(2)e Ff(G)j Fg(sei)818 886 y Ff(L)851 893 y Fd(g)885 886 y Fg(:)c Ff(G)h Fe(!)g Ff(G;)8 b(h)14 b Fe(7!)g Ff(g)r(h)284 983 y Fg(die)j(Linksm)o(ultiplik) l(ation)f(mit)g Ff(g)r Fg(.)h(Zeigen)g(Sie,)g(da\031)h Ff(L)1319 990 y Fd(g)1357 983 y Fg(bijektiv)e(ist)i(und)g(da\031)284 1043 y(die)d(Abbildung)748 1103 y Ff(L)f Fg(:)g Ff(G)g Fe(!)g Fg(Bij)o(\()p Ff(G;)8 b(G)p Fg(\))p Ff(;)g(g)16 b Fe(7!)e Ff(L)1296 1110 y Fd(g)284 1185 y Fg(ein)22 b(injektiv)o(er)e(Grupp)q(enhomomorphism)o(us)g(ist.)i(\(Hin)o(w)o (eis:)f(Dieser)h(Homo-)284 1245 y(morphism)o(us)11 b(wird)h(auc)o(h)h (als)h(Ca)o(yley-Darstellung)e(b)q(ezeic)o(hnet.)f(Er)i(zeigt,)f (da\031)284 1305 y(jede)h(endlic)o(he)f(Grupp)q(e)i(zu)g(einer)f(Un)o (tergrupp)q(e)h(einer)e(symmetrisc)n(hen)f(Grup-)284 1365 y(p)q(e)16 b(isomorph)g(ist.\))1071 b(\(5\))197 1463 y(22.)25 b(Sei)15 b Ff(G)i Fg(eine)e(Grupp)q(e)i(und)g Ff(N)i Fe(\032)13 b Ff(G)k Fg(ein)f(Normalteiler.)c(F)1366 1465 y(\177)1365 1463 y(ur)17 b Ff(g)f Fe(2)e Ff(G)i Fg(sei)772 1560 y Ff(K)813 1567 y Fd(g)847 1560 y Fg(:)e Ff(N)19 b Fe(!)13 b Ff(N)r(;)8 b(n)15 b Fe(7!)e Ff(g)r(ng)1245 1539 y Fc(\000)p Fb(1)284 1657 y Fg(die)i(Konjugation)j(mit)c Ff(g)r Fg(.)304 1755 y(\(a\))25 b(Zeigen)13 b(Sie,)g(da\031)i Ff(K)764 1762 y Fd(g)799 1755 y Fg(ein)e(Automorphism)o(us,)f(also)i (ein)g(bijektiv)o(er)d(Grup-)391 1815 y(p)q(enhomomorphism)o(us)j(ist.) 302 1892 y(\(b\))24 b(Zeigen)16 b(Sie,)f(da\031)i(die)e(Abbildung)809 1989 y Ff(K)j Fg(:)c Ff(G)g Fe(!)g Fg(Aut)o(\()p Ff(N)5 b Fg(\))p Ff(;)j(g)16 b Fe(7!)e Ff(K)1342 1996 y Fd(g)391 2085 y Fg(ein)j(Grupp)q(enhomomorphism)o(us)e(in)i(die)f(Grupp)q(e)i (Aut\()p Ff(N)5 b Fg(\))17 b(aller)g(Auto-)391 2145 y(morphismen)d(v)o (on)i Ff(N)21 b Fg(ist.)307 2223 y(\(c\))j(Konstruieren)12 b(Sie)g(ein)g(Beispiel)f(f)1024 2225 y(\177)1023 2223 y(ur)h(einen)g(Normalteiler)d(in)k(einer)e(Grup-)391 2283 y(p)q(e,)16 b(f)487 2285 y(\177)486 2283 y(ur)g(den)g(die)g (Abbildung)g Ff(K)k Fg(nic)o(h)o(t)15 b(injektiv)g(ist.)332 b(\(6\))197 2381 y(23.)25 b(Eine)f(F)l(unktion)g Ff(f)33 b Fg(:)27 b Fa(R)d Fe(!)k Fa(R)21 b Fg(hei\031t)j(gerade,)g(w)o(enn)g (f)1375 2383 y(\177)1374 2381 y(ur)h(alle)e Ff(x)k Fe(2)h Fa(R)21 b Fg(die)284 2441 y(Gleic)o(h)o(ung)16 b Ff(f)5 b Fg(\()p Fe(\000)p Ff(x)p Fg(\))15 b(=)h Ff(f)5 b Fg(\()p Ff(x)p Fg(\))18 b(gilt.)e(Sie)h(hei\031t)g(ungerade,)g(w)o(enn)g(f)1499 2443 y(\177)1498 2441 y(ur)h(alle)e Ff(x)g Fe(2)g Fa(R)284 2501 y Fg(die)f(Gleic)o(h)o(ung)g Ff(f)5 b Fg(\()p Fe(\000)p Ff(x)p Fg(\))14 b(=)g Fe(\000)p Ff(f)5 b Fg(\()p Ff(x)p Fg(\))16 b(gilt.)p eop %%Page: 2 2 2 1 bop 304 274 a Fg(\(a\))25 b(Zeigen)19 b(Sie,)g(da\031)i(die)e (Mengen)h Ff(F)1042 281 y Fd(G)1091 274 y Fg(und)h Ff(F)1225 281 y Fd(U)1274 274 y Fg(aller)e(geraden)h(bzw.)g(aller)391 334 y(ungeraden)d(F)l(unktionen)f(Un)o(terv)o(ektorr)1161 336 y(\177)1161 334 y(aume)d(des)j(Raumes)f(Abb\()p Fa(R)p Ff(;)8 b Fa(R)m Fg(\))391 394 y(aller)16 b(F)l(unktionen)f(v)o(on)h Fa(R)e Fg(nac)o(h)i Fa(R)d Fg(sind.)302 475 y(\(b\))24 b(Zeigen)c(Sie,)g(da\031)h(jede)f(F)l(unktion)h(als)g(Summe)d(einer)h (geraden)i(und)g(ei-)391 535 y(ner)f(ungeraden)h(F)l(unktion)f (dargestellt)g(w)o(erden)f(k)m(ann,)i(und)f(da\031)i(diese)391 596 y(Darstellung)17 b(eindeutig)e(ist.)787 b(\(5\))197 697 y(24.)25 b(Sei)15 b Ff(a)f Fe(2)g Fa(R)f Fg(eine)i(reelle)g(Zahl.)g (Betrac)o(h)o(te)g(die)g(Menge)562 807 y Ff(V)590 814 y Fd(a)625 807 y Fg(:=)f Fe(f)p Fg(\()p Ff(x)763 814 y Fb(1)782 807 y Ff(;)8 b(x)832 814 y Fb(2)851 807 y Ff(;)g(x)901 814 y Fb(3)921 807 y Fg(\))13 b Fe(2)i Fa(R)1039 787 y Fb(3)1070 807 y Fe(j)f Fg(2)p Ff(x)1150 814 y Fb(1)1181 807 y Fe(\000)c Ff(x)1258 814 y Fb(2)1289 807 y Fe(\000)h Ff(x)1367 814 y Fb(3)1400 807 y Fg(=)j Ff(a)p Fe(g)284 917 y Fg(Bestimm)o(en)8 b(Sie)j(diejenigen)f(Zahlen)h Ff(a)i Fe(2)h Fa(R)p Fg(,)8 b(f)1149 919 y(\177)1148 917 y(ur)k(die)e Ff(V)1307 924 y Fd(a)1340 917 y Fg(ein)h(Un)o(terv)o (ektorraum)284 978 y(v)o(on)16 b Fa(R)415 960 y Fb(3)448 978 y Fg(ist.)1204 b(\(4\))162 1092 y(Abgab)q(e:)15 b(Mitt)o(w)o(o)q(c) o(h,)e(6.12.2000,)j(12.00)g(Uhr,)1052 1081 y(\177)1045 1092 y(Ubungsk)1232 1094 y(\177)1232 1092 y(asten)g(im)d(1.)h(Sto)q(c)o (k)h(des)f(Ma-)162 1152 y(thematisc)o(hen)g(Instituts.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF