Dear Sven,
Now I see the way to find out what f1,f2,f3 exactly are in the A4 group! Thank you so much for your help! Best regards, Jiayue > -----原始邮件----- > 发件人: "Sven Reichard" <sven.reich...@tu-dresden.de> > 发送时间: 2016年12月21日 星期三 > 收件人: fo...@gap-system.org > 抄送: > 主题: Re: [GAP Forum] AlternatingGroup(4) and its generators > > Dear Jiayue, > > to be precise, G is isomorphic to the alternating group. You can find > such an isomorphism and determine the images of the generators as follows: > > gap> G := SmallGroup(12,3); > <pc group of size 12 with 3 generators> > gap> StructureDescription(G); > "A4" > gap> a4 := AlternatingGroup(4); > Alt( [ 1 .. 4 ] ) > gap> iso := IsomorphismGroups(G, a4); > [ f1, f2, f3 ] -> [ (2,4,3), (1,3)(2,4), (1,2)(3,4) ] > gap> List(GeneratorsOfGroup(G), g -> Image(iso, g)); > [ (2,4,3), (1,3)(2,4), (1,2)(3,4) ] > > HTH, > Sven > > On 21.12.2016 12:40, 齐嘉悦 wrote: > > > > Dear Forum members, > > > > > > When I type this in GAP: > > > > > > gap>G:=SmallGroup(12,3); > > gap>GeneratorsOfGroup(G); > > the result is [f1,f2,f3],but actually the group G here is > > AlternatingGroup(4) and I wonder > > how could I know here what f1,f2,f3 exactly means by permutations > > respectively? How > > could I know what are they in A4? > > > > > > Looking forward to any reply! > > > > > > Thanks a lot! > > > > > > Jiayue > > > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum > > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
