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(k)m(onstan)m(t)g(gleic)m(h)f(der)h(iden)m(tisc)m(hen)g(Abbildung)f(v)m (on)h Fb(Z)3526 4477 y Fa(q)782 4582 y Fg(ist.)41 b(Konstruieren)h(Sie) f(damit)e(eine)j(nic)m(h)m(tab)s(elsc)m(he)g(Grupp)s(e)f(der)h(Ord-)782 4702 y(n)m(ung)33 b Ff(pq)k Fg(als)32 b(semidirektes)g(Pro)s(dukt.)603 4864 y(\(b\))49 b(Zeigen)41 b(Sie,)g(da\031)h(sic)m(h)f(jede)i(nic)m(h) m(tab)s(elsc)m(he)f(Grupp)s(e)g(der)g(Ordn)m(ung)g Ff(pq)782 4985 y Fg(isomorph)32 b(zu)h(einer)f(der)h(ob)s(en)g(k)m(onstruierten)g (Grupp)s(en)g(ist.)p eop %%Page: 2 2 2 1 bop 614 548 a Fg(\(c\))49 b(Zeigen)44 b(Sie,)f(da\031)h(je)g(zw)m (ei)h(nic)m(h)m(tab)s(elsc)m(he)g(Grupp)s(en)f(der)g(Ordn)m(ung)h Ff(pq)782 668 y Fg(isomorph)32 b(sind.)568 872 y(\(Hin)m(w)m(eis:)h(V) -8 b(erw)m(enden)34 b(Sie)f(Aufgab)s(e)f(19.\))1240 b(\(6\))394 1075 y(27.)49 b(Sei)34 b Ff(G)g Fg(eine)h(Grupp)s(e)g(und)g Ff(Z)7 b Fg(\()p Ff(G)p Fg(\))34 b(ihr)g(Zen)m(trum.)h(Zeigen)f(Sie:)g (W)-8 b(enn)36 b Ff(G=)-5 b(Z)7 b Fg(\()p Ff(G)p Fg(\))568 1196 y(zyklisc)m(h)33 b(ist,)f(dann)h(ist)f Ff(G)h Fg(ab)s(elsc)m(h.) 1514 b(\(3\))394 1399 y(28.)49 b(Sei)32 b Ff(i)c Fg(=)889 1321 y Fe(p)p 972 1321 127 4 v 78 x(\000)p Fg(1)g Fe(2)g Fb(C)59 b Fg(und)33 b Ff(R)c Fg(=)e Fb(Z)p Fg([)p Ff(i)p Fg(])f(=)h Fe(f)p Ff(a)c Fg(+)f Ff(b)17 b(i)g Fe(j)g Ff(a;)g(b)27 b Fe(2)h Fb(Z)p Fe(g)p Fg(.)609 1602 y(\(a\))48 b(Man)33 b(zeige,)g(da\031)f Ff(R)i Fg(ein)e(Un)m(terring)g(v)m(on)h Fb(C)59 b Fg(ist.)603 1764 y(\(b\))49 b(Betrac)m(h)m(te)34 b(die)e(Abbildung)1544 1984 y Ff(\016)f Fg(:)d Ff(R)h Fe(!)e Fb(N)1969 1999 y Fc(0)2015 1984 y Ff(;)49 b(a)22 b Fg(+)g Ff(b)17 b(i)28 b Fe(7!)f Ff(a)2559 1943 y Fc(2)2621 1984 y Fg(+)22 b Ff(b)2760 1943 y Fc(2)782 2204 y Fg(Man)33 b(zeige,)g(da\031)f(da\031)g(\()p Ff(R)q(;)17 b(\016)t Fg(\))32 b(ein)g(euklidisc)m(her)h(Ring)f(ist.)614 2366 y(\(c\))49 b(Man)33 b(b)s(estimme)e(die)i(Einheitengrupp)s(e)f Ff(R)2417 2330 y Fd(\003)2457 2366 y Fg(.)953 b(\(5\))324 2594 y(Abgab)s(e:)37 b(Dienstag,)g(7.1.2003,)f(11.15)h(Uhr,)2063 2573 y(\177)2051 2594 y(Ubungsk)2424 2598 y(\177)2424 2594 y(asten)j(im)35 b(1.)j(Sto)s(c)m(k)g(des)g(Ma-)324 2715 y(thematisc)m(hen)33 b(Instituts.)324 2835 y(Bitte)f(geb)s(en)h (Sie)f(auf)g(Ihrer)h(L)1475 2839 y(\177)1475 2835 y(osung)g(Ihren)h (Namen)e(und)h(Ihre)2753 2814 y(\177)2741 2835 y(Ubungsgrupp)s(e)h(an.) 324 3192 y(Wir)43 b(w)606 3196 y(\177)603 3192 y(unsc)m(hen)j(allen)c (V)-8 b(orlesungsteilnehmern)43 b(fr)2302 3196 y(\177)2302 3192 y(ohlic)m(he)f(W)-8 b(eihnac)m(h)m(ten)45 b(und)f(ein)324 3312 y(gutes)33 b(neues)h(Jahr.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF