7.12 Subgroup

Subgroup( G, L )

Let G be a parent group and L be a list of elements g_1, ..., g_n of G. Subgroup returns the subgroup U generated by g_1, ..., g_n with parent group G.

Note that this function is the only group function in which the name Subgroup does not refer to the mathematical terms subgroup and supergroup but to the implementation of groups as subgroups and parent groups. IsSubgroup (see IsSubgroup) is not the negation of IsParent (see IsParent) but decides subgroup and supergroup relations.

Subgroup always binds a copy of L to U.generators, so it is safe to modify L after calling Subgroup because this will not change the entries in U.

Let g_{i_1}, ..., g_{i_m} be the nontrivial generators. Subgroups binds these generators to U.1, ..., U.m.

    gap> s4 := Group( (1,2,3,4), (1,2) );
    Group( (1,2,3,4), (1,2) )
    gap> v4 := Subgroup( s4, [ (1,2), (1,2)(3,4) ] );
    Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,2), (1,2)(3,4) ] )
    gap> IsParent( v4 );
    false 

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