{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "MS Sans Serif" 1 8 128 0 128 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "MS Sans Serif" 1 9 0 128 128 1 2 2 2 0 0 2 0 0 0 1 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti mes" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 9 128 0 128 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 8 0 128 128 1 1 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Seitenumbruch" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 1 2 0 1 }{PSTYLE "Normal" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 261 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 262 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 9 "Algebra 1" }}{PARA 0 "" 0 "" {TEXT 257 9 "SOSe 2004" }}{PARA 0 "" 0 "" {TEXT 258 74 "Bestimmung der Gruppenordnung in Aufgabe (5) mit dem Maple-Paket \"group\":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "with(group); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7> %)DerivedSG%$LCSG%.NormalClosureG%,RandElementG%-SnConjugatesG%&SylowG %-areconjugateG%'centerG%,centralizerG%%coreG%'cosetsG%'cosrepG%(deriv edG%)elementsG%,groupmemberG%+grouporderG%&interG%(invpermG%*isabelian G%)isnormalG%+issubgroupG%)mulpermsG%+normalizerG%&orbitG%'parityG%(pe rmrepG%%presG%+transgroupG" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 71 "U m die Definition der Gruppe treffen zu k\366nnen, muss man sich der Za hl " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 25 " entledigen. E s gilt ja " }{XPPEDIT 18 0 "B*A*B^(-1) = alpha*A;" "6#/*(%\"BG\"\"\"% \"AGF&)F%,$F&!\"\"F&*&%&alphaGF&F'F&" }{TEXT -1 8 " , und " } {XPPEDIT 18 0 "alpha*A*` A`^2 = alpha*E;" "6#/*(%&alphaG\"\"\"%\"AGF&) %#~AG\"\"#F&*&F%F&%\"EGF&" }{TEXT -1 13 " , also ist " }{XPPEDIT 18 0 "C = alpha*E;" "6#/%\"CG*&%&alphaG\"\"\"%\"EGF'" }{TEXT -1 17 " in \+ der Gruppe !" }}{PARA 262 "" 0 "" {TEXT -1 50 "Ich definiere daher die Gruppe ohne Benutzung von " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" } {TEXT -1 11 " wie folgt:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "G:=grelgroup(\{A,B,C\}, \{[A,A,A], [B,B,B], [C,C,C],[A,B,1/A,1/C,1/B,1/C],[A,C,1/A,1/C],[B,C,1/B,1/C]\}) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG-%*grelgroupG6$<%%\"AG%\"BG %\"CG<(7%F)F)F)7%F*F*F*7%F+F+F+7(F)F**&\"\"\"F2F)!\"\"*&F2F2F+F3*&F2F2 F*F3F47&F)F+F1F47&F*F+F5F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "Erl \344uterungen von Maple zu den Anweisungen erhalten Sie, wenn Sie den \+ Kursor z.B. auf " }{TEXT 0 9 "grelgroup" }{TEXT -1 29 " setzen und \+ dann F1 dr\374cken." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "grou porder(G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#F" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "U:=subgrel(\{x=[]\},G);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"UG-%(subgrelG6$<#/%\"xG7\"-%*grelgroupG6$<%%\"AG% \"BG%\"CG<(7%F0F0F07%F1F1F17%F2F2F27(F0F1*&\"\"\"F9F0!\"\"*&F9F9F2F:*& F9F9F1F:F;7&F0F2F8F;7&F1F2F " 0 "" {MPLTEXT 1 0 10 "cosets(U);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<=7\"7#%\"CG7$% \"BGF(7&%\"AGF*F(F(7#F*7#F(7$F*F(7%F*F(*&\"\"\"F0F*!\"\"7&F*F(F/*&F0F0 F&F17$F*F*7$F&F&7$F*F&7%F*F(F(7%F*F&F&7%F*F*F(7&F*F*F(F/7'F*F*F(F/F37% F*F*F&7&F*F*F&F&7$F(F/7%F(F/F37%F(F*F(7&F(F*F(F/7'F(F*F(F/F37%F(F(F*7& F(F(F*F*7&F*F(F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nops(% );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#F" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "9 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }