Type: Article

Two nonisomorphic groups of order 96 with isomorphic tables of marks and noncorresponding centres and abelian subgroups

Alberto Raggi-Cárdenas; Luis Valero-Elizondo;

Abstract:

We construct two nonisomorphic groups G and Q of order 96 which have isomorphic tables of marks, but such that the centre of G has order 8 and the centre of Q has order 4. We also note that G has an abelian subgroup of order 48, whereas Q has no abelian subgroup of that order. This also leads us to conclude that this isomorphism of tables of marks does not preserve normalizers.