Hi Chris They are isomorphic groups, so they have the same name. In both cases they’re the alternating and symmetric groups on 5 points; the ones of degree 5 are the natural action, the ones of degree 10 are the actions on unordered pairs. In general any group has multiple primitive actions.
Best wishes Colva On 10 Nov 2013, at 19:54, Chris Jefferson <ca...@st-andrews.ac.uk> wrote: > After trying to track down some strange behavior in a program, I was > surprised to find the names of the first two primitive groups of size 10: > > gap> PrimitiveGroup(10, 1); > A(5) > gap> PrimitiveGroup(10, 2); > S(5) > > These are, unsurprisingly, the same names as: > > gap> PrimitiveGroup(5,4); > A(5) > gap> PrimitiveGroup(5,5); > S(5) > > Out of curiosity, are these groups related in some non-obvious way, and is > there any reason the names of the primitive groups are not unique? > > Chris > > > _______________________________________________ > 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
