Year: 2009
Type: article
Abstract: . 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.
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W208336906