%!PS-Adobe-2.0 %%Creator: dvips 5.58 Copyright 1986, 1994 Radical Eye Software %%Title: ln43.dvi %%CreationDate: Mon Jun 26 16:21:20 2000 %%Pages: 5 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: DVIPS16 -a ln43 %DVIPSParameters: dpi=300, compressed, comments removed %DVIPSSource: TeX output 2000.06.26:1534 %%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 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Fk(p)p Fe(\))p Fd(\012)p Fe(\(1)p Fd(\012)p Fk(p)p Fe(\))p 1269 1928 V 1270 1928 a Fa(?)1289 1872 y Fe(1)p Fd(\012)p Fk(p)0 2058 y Fq(W)l(e)16 b(iden)o(tify)f (elemen)o(ts)f(along)j(the)f(isomorphisms.)k(Th)o(us)d(w)o(e)f(get)g (\(\001)1337 2065 y Fk(H)1382 2058 y Fj(\012)11 b Fq(1)28 b(\)\(1)1546 2065 y Fk(H)1591 2058 y Fj(\012)11 b Fl(p)p Fq(\)\()p Fl(g)r Fq(\))k(=)0 2117 y(\(1)43 2124 y Fk(H)s Fd(\012)p Fk(H)149 2117 y Fj(\012)e Fl(p)p Fq(\)\(\001)304 2124 y Fk(H)350 2117 y Fj(\012)g Fq(1)452 2124 y Fe(\()p Fk(\016)q Fe(\))498 2117 y Fq(\)\()p Fl(g)r Fq(\))19 b(=)f(\(\(1)717 2124 y Fk(H)764 2117 y Fj(\012)13 b Fl(p)p Fq(\))g Fj(\012)937 2124 y Fe(\()p Fk(\016)q Fe(\))996 2117 y Fq(\(1)1039 2124 y Fk(H)1086 2117 y Fj(\012)g Fl(p)p Fq(\)\)\()p Fl(g)i Fj(\012)1322 2124 y Fe(\()p Fk(\016)q Fe(\))1381 2117 y Fl(g)r Fq(\))k(=)f(\(1)1543 2124 y Fk(H)1590 2117 y Fj(\012)13 b Fl(p)p Fq(\)\()p Fl(g)r Fq(\))g Fj(\012)0 2175 y Fq(\(1)43 2182 y Fk(H)84 2175 y Fj(\012)7 b Fl(p)p Fq(\)\()p Fl(g)r Fq(\),)14 b(so)g(that)h(1)449 2182 y Fk(H)490 2175 y Fj(\012)7 b Fl(p)13 b Fq(:)h Fl(G)665 2182 y Fe(\()p Fk(\016)q Fe(\))711 2175 y Fq(\()p Fl(H)d Fj(\012)46 b Fq(\()p Fl(\016)r Fq(\)\))13 b Fj(\000)-31 b(!)14 b Fl(G)p Fq(\()p Fl(H)t Fq(\).)21 b(No)o(w)14 b(w)o(e)g(ha)o(v)o(e)f(\(1)1519 2182 y Fk(H)1560 2175 y Fj(\012)7 b Fl(p)p Fq(\)\()p Fl(g)r(g)1718 2157 y Fd(0)1729 2175 y Fq(\))14 b(=)0 2233 y(\(1)43 2240 y Fk(H)88 2233 y Fj(\012)d Fl(p)p Fq(\)\()p Fl(g)r Fq(\)\(1)287 2240 y Fk(H)332 2233 y Fj(\012)g Fl(p)p Fq(\)\()p Fl(g)469 2215 y Fd(0)481 2233 y Fq(\))17 b(so)g(that)f(1)706 2240 y Fk(H)751 2233 y Fj(\012)11 b Fl(p)17 b Fq(is)f(a)h(group)g(homomorphism.)75 2291 y(No)o(w)d(let)g Fl(g)i Fq(=)e Fl(g)367 2298 y Fe(0)395 2291 y Fj(\012)8 b Fq(1)g(+)g Fl(g)543 2298 y Fe(1)572 2291 y Fj(\012)g Fl(\016)15 b Fj(2)f Fl(G)767 2299 y Fe(\()p Fk(\016)q Fe(\))814 2291 y Fq(\()p Fl(H)f Fj(\012)47 b Fq(\()p Fl(\016)r Fq(\)\))12 b Fj(\022)i Fl(H)e Fj(\012)55 b(\010)8 b Fl(H)13 b Fj(\012)47 b Fl(\016)r Fq(.)19 b(Then)c(w)o(e)g (ha)o(v)o(e)0 2349 y(\(1)43 2356 y Fk(H)88 2349 y Fj(\012)c Fl(p)p Fq(\)\()p Fl(g)r Fq(\))j(=)g(1)j(i\013)f Fl(g)432 2356 y Fe(0)466 2349 y Fq(=)e(1)i(i\013)g Fl(g)g Fq(=)e(1)731 2356 y Fk(H)776 2349 y Fj(\012)d Fq(1)876 2357 y Fe(\()p Fk(\016)q Fe(\))934 2349 y Fq(+)g Fl(g)1006 2356 y Fe(1)1037 2349 y Fj(\012)g Fl(\016)r Fq(.)20 b(F)l(urthermore)15 b(w)o(e)h(ha)o(v)o(e)43 2433 y(\001)84 2440 y Fk(H)s Fd(\012)26 b Fe(\()p Fk(\016)q Fe(\))215 2433 y Fq(\()p Fl(g)r Fq(\))13 b(=)h Fl(g)f Fj(\012)444 2440 y Fe(\()p Fk(\016)q Fe(\))501 2433 y Fl(g)j Fj(\()-8 b(\))43 2491 y Fq(1)67 2498 y Fk(H)112 2491 y Fj(\012)11 b Fq(1)186 2498 y Fk(H)231 2491 y Fj(\012)f Fq(1)330 2498 y Fe(\()p Fk(\016)q Fe(\))388 2491 y Fq(+)h(\001)478 2498 y Fk(H)511 2491 y Fq(\()p Fl(g)553 2498 y Fe(1)573 2491 y Fq(\))g Fj(\012)g Fl(\016)16 b Fq(=)d(\(1)785 2498 y Fk(H)830 2491 y Fj(\012)e Fq(1)930 2498 y Fe(\()p Fk(\016)q Fe(\))988 2491 y Fq(+)g Fl(g)1060 2498 y Fe(1)1091 2491 y Fj(\012)g Fl(\016)r Fq(\))f Fj(\012)1259 2498 y Fe(\()p Fk(\016)q Fe(\))1316 2491 y Fq(\(1)1359 2498 y Fk(H)1404 2491 y Fj(\012)h Fq(1)1504 2498 y Fe(\()p Fk(\016)q Fe(\))1562 2491 y Fq(+)g Fl(g)1634 2498 y Fe(1)1665 2491 y Fj(\012)g Fl(\016)r Fq(\))389 2549 y(=)j(1)465 2556 y Fk(H)510 2549 y Fj(\012)d Fq(1)584 2556 y Fk(H)629 2549 y Fj(\012)g Fq(1)729 2557 y Fe(\()p Fk(\016)q Fe(\))786 2549 y Fq(+)g(\()p Fl(g)877 2556 y Fe(1)908 2549 y Fj(\012)g Fq(1)982 2556 y Fk(H)1027 2549 y Fq(+)g(1)1100 2556 y Fk(H)1145 2549 y Fj(\012)g Fl(g)1218 2556 y Fe(1)1238 2549 y Fq(\))g Fj(\012)g Fl(\016)k Fj(\()-8 b(\))43 2607 y Fq(\001)84 2614 y Fk(H)117 2607 y Fq(\()p Fl(g)159 2614 y Fe(1)179 2607 y Fq(\))14 b(=)g Fl(g)287 2614 y Fe(1)318 2607 y Fj(\012)d Fq(1)392 2614 y Fk(H)437 2607 y Fq(+)g(1)510 2614 y Fk(H)555 2607 y Fj(\012)g Fl(g)628 2614 y Fe(1)648 2607 y Fl(:)p eop %%Page: 139 5 139 4 bop 429 118 a Fo(3.)17 b(THE)g(LIE)f(ALGEBRA)h(OF)g(PRIMITIVE)f (ELEMENTS)359 b(139)0 213 y Fq(Similarly)13 b(w)o(e)j(ha)o(v)o(e)g Fl(")441 220 y Fe(\()p Fk(\016)q Fe(\))487 213 y Fq(\)\()p Fl(g)r Fq(\))d(=)h(1)j(i\013)f(1)c Fj(\012)e Fq(1)i(+)f Fl(")p Fq(\()p Fl(g)968 220 y Fe(1)988 213 y Fq(\))g Fj(\012)g Fl(\016)k Fq(=)f(1)i(i\013)h Fl(")p Fq(\()p Fl(g)1321 220 y Fe(1)1340 213 y Fq(\))d(=)g(0.)p 1765 213 2 33 v 1767 181 30 2 v 1767 213 V 1796 213 2 33 v eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF