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
