Thanks. I should have consulted the manual first. Still think it is strange that StructureDescription does not determine the group up to isomorphism.
R.E. Boss > -----Oorspronkelijk bericht----- > Van: Stephen Linton [mailto:s...@cs.st-andrews.ac.uk] > Verzonden: maandag 20 augustus 2012 10:03 > Aan: R.E. Boss > CC: fo...@gap-system.org > Onderwerp: Re: [GAP Forum] Equal structure descriptions > > Dear GAP Forum, > > R.E. Boss asked about non-isomorphic groups with equal structure descriptions. > This CAN happen. The manual entry for "StructureDescription" > > http://www.gap-system.org/Manuals/doc/ref/chap39.html#X8199B74B84446971 > > says: > > "The string returned by StructureDescription is <not> an isomorphism > invariant: non-isomorphic groups can have the same string value, and two > isomorphic groups in different representations can produce different > strings." > > StructureDescription provides an "informal" overview of the structure of a > group, which is a useful > first view for small groups. More sophisticated function in the same area > include IdGroup; > the StandardPresentation function of the anupq package and IsomorphismGroups, > each of which is described > in the appropriate manual. > > Yours > > Steve Linton > > On 20 Aug 2012, at 08:00, R.E. Boss wrote: > > > What can I conclude from the equal structure descriptions below I stumbled > > upon? > > > > > > > > R.E. Boss > > > > > > > > > > > > gap> StructureDescription(SmallGroup(64,156)); > > > > "Q8 : Q8" > > > > gap> StructureDescription(SmallGroup(64,158)); > > > > "Q8 : Q8" > > > > > > > > gap> StructureDescription(SmallGroup(64,155)); > > > > "(C8 : C4) : C2" > > > > gap> StructureDescription(SmallGroup(64,157)); > > > > "(C8 : C4) : C2" > > > > gap> StructureDescription(SmallGroup(64,159)); > > > > "(C8 : C4) : C2" > > > > > > > > gap> StructureDescription(SmallGroup(64,160)); > > > > "(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)" > > > > gap> StructureDescription(SmallGroup(64,179)); > > > > "C8 : Q8" > > > > gap> StructureDescription(SmallGroup(64,180)); > > > > "(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)" > > > > > > > > _______________________________________________ > > 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
