7.13 AsSubgroup

AsSubgroup( G, U )

Let G be a parent group and U be a parent group or a subgroup with a possibly different parent group, such that the generators g_1, ..., g_n of U are elements of G. AsSubgroup returns a new subgroup S such that S has parent group G and is generated by g_1, ..., g_n.

    gap> d8 := Group( (1,2,3,4), (1,2)(3,4) );
    Group( (1,2,3,4), (1,2)(3,4) )
    gap> z := Centre( d8 );
    Subgroup( Group( (1,2,3,4), (1,2)(3,4) ), [ (1,3)(2,4) ] )
    gap> s4 := Group( (1,2,3,4), (1,2) );
    Group( (1,2,3,4), (1,2) )
    gap> Normalizer( s4, AsSubgroup( s4, z ) );
    Subgroup( Group( (1,2,3,4), (1,2) ), [ (2,4), (1,2,3,4), (1,3)(2,4)
     ] ) 

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