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b Fe(\032)55 b Fg(F)63 b Fh(eine)48 b(K)1650 2705 y(\177)1650 2701 y(orp)s(ererw)m(eiterung)h(und)g Fg(G)55 b Fe(\032)g Fh(Aut\()p Fg(F)8 b(=K)f Fh(\))49 b(eine)782 2822 y(\(nic)m(h)m(t)39 b(not)m(w)m(endig)g(endlic)m(he\))g(Un)m(tergrupp)s(e)g(mit)e Fg(K)45 b Fh(=)38 b(Fix)o(\()p Fg(F)s(;)17 b(G)p Fh(\).)38 b(Sei)782 2942 y Fg(p)28 b Fe(2)g Fg(F)14 b Fh([)p Fg(x)p Fh(])22 b(ein)g(P)m(olynom.)f(Zeigen)g(Sie,)g(da\031)h Fg(p)g Fh(genau)g(dann)g(b)s(ereits)g(in)f Fg(K)7 b Fh([)p Fg(x)p Fh(])782 3062 y(liegt,)31 b(w)m(enn)39 b(^)-54 b Fg(\033)t Fh(\()p Fg(p)p Fh(\))28 b(=)f Fg(p)33 b Fh(f)1708 3066 y(\177)1705 3062 y(ur)f(alle)f Fg(\033)h Fe(2)c Fg(G)k Fh(gilt.)614 3224 y(\(c\))49 b(Sei)f Fg(K)62 b Fe(\032)55 b Fg(F)63 b Fh(eine)48 b(K)1650 3228 y(\177)1650 3224 y(orp)s(ererw)m(eiterung)h(und)g Fg(G)55 b Fe(\032)g Fh(Aut\()p Fg(F)8 b(=K)f Fh(\))49 b(eine)782 3345 y(\(nic)m(h)m(t)39 b(not)m(w)m(endig)g(endlic)m(he\))g(Un)m(tergrupp)s(e)g(mit)e Fg(K)45 b Fh(=)38 b(Fix)o(\()p Fg(F)s(;)17 b(G)p Fh(\).)38 b(Sei)782 3465 y Fg(a)28 b Fe(2)g Fg(F)14 b Fh(.)28 b(Zeigen)g(Sie,)f (da\031)h Fg(a)h Fh(genau)f(dann)g(algebraisc)m(h)2847 3469 y(\177)2845 3465 y(ub)s(er)g Fg(K)35 b Fh(ist,)28 b(w)m(enn)782 3585 y(die)k(Bahn)h Fe(f)p Fg(\033)t Fh(\()p Fg(a)p Fh(\))28 b Fe(j)f Fg(\033)32 b Fe(2)c Fg(G)p Fe(g)k Fh(endlic)m(h)g(ist.)1116 b(\(6\))324 3814 y(Abgab)s(e:)28 b(Dienstag,)e(26.11.2002,)g(11.15)h(Uhr,)2112 3792 y(\177)2100 3814 y(Ubungsk)2473 3818 y(\177)2473 3814 y(asten)j(im)c(1.)h(Sto)s(c)m (k)h(des)h(Ma-)324 3934 y(thematisc)m(hen)k(Instituts.)324 4054 y(Bitte)f(geb)s(en)h(Sie)f(auf)g(Ihrer)h(L)1475 4058 y(\177)1475 4054 y(osung)g(Ihren)h(Namen)e(und)h(Ihre)2753 4033 y(\177)2741 4054 y(Ubungsgrupp)s(e)h(an.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF