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8.1 Groups and actions

  • OnSubgroups( subgroup, aut ) F

    For a group G and an automorphism aut of G, OnSubgroups(subgroup,aut) is the image of subgroup under aut

    gap> G:=Group((1,2,3),(2,3));
    Group([ (1,2,3), (2,3) ])
    gap> alpha:=InnerAutomorphism(G,(1,2,3));
    ^(1,2,3)
    gap> OnSubgroups(Subgroup(G,[(2,3)]),alpha);
    Group([ (1,3) ])
    

  • RepsCClassesGivenOrder( group, order ) O

    RepsCClassesGivenOrder( group, order ) returns all elements of order order up to conjugacy. Note that the representatives are not always the smallest elements of each conjugacy class.

    gap> RepsCClassesGivenOrder(SymmetricGroup(5),2);
    [ (4,5), (2,3)(4,5) ]
    

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    RDS manual
    November 2006