GAP Manual: 7.52. IsAbelian

IsAbelian( G )

IsAbelian returns true if the group G is abelian and false otherwise.

A group G is abelian if and only if for every g, hinG the equation g* h = h* g holds.

Note that IsAbelian sets and tests the record component G.isAbelian. If G is abelian it also sets G.centre.

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

The default group function GroupOps.IsAbelian returns true for a group G generated by g_1, ..., g_n if g_i commutes with g_j for i > j.