Abstract

HUERTA-APARICIO, LUIS; MOLINA-RUEDA, ARIEL; RAGGI-CARDENAS, ALBERTO  and  VALERO-ELIZONDO, LUIS. On some invariants preserved by isomorphisms of tables of marks. Rev.colomb.mat. [online]. 2009, vol.43, n.2, pp.165-174. ISSN 0034-7426.

Let G and Q be groups with isomorphic tables of marks, and for each subgroup H of G, let H' denote a subgroup of Q assigned to H under an isomorphism between the tables of marks of G and Q. We prove that if H is cyclic/elementary abelian/maximal/the Frattini subgroup/the commutator subgroup, then H' has the same property. However, we give examples where H is abelian and H' is not, and where H is the centre of G and H' is not the centre of Q. For this we construct (using GAP) the smallest example of non-isomorphic groups with isomorphic tables of marks.

Keywords : Group representation; Burnside rings; table of marks.

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