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2023•Communications in AlgebraRequires access

Groups with isomorphic fibered Burnside rings

Robert Boltje, Benjamin García

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Abstract

Let G and H be finite groups. We give a condition on G and H that implies that the A-fibered Burnside rings BA(G) and BA(H) are isomorphic. As a consequence, we show the existence of non-isomorphic groups G and H such that BA(G) and BA(H) are isomorphic rings. Here, the abelian fiber group A can be chosen in a non-trivial way, that is, such that BA(G) and BA(H) are strictly bigger than the Burnside rings of G and H, for which such counterexamples are already known.Communicated by Mandi Schaeffer Fry

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Let G and H be finite groups. We give a condition on G and H that implies that the A-fibered Burnside rings BA(G) and BA(H) are isomorphic. As a consequence, we show the existence of non-isomorphic groups G and H such that BA(G) and BA(H) are isomorphic rings. Here, the abelian fiber group A can be chosen in a non-trivial way, that is, such that BA(G) and BA(H) are strictly bigger than the Burnside rings of G and H, for which such counterexamples are already known.Communicated by Mandi Schaeffer Fry

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Available abstract

Let G and H be finite groups. We give a condition on G and H that implies that the A-fibered Burnside rings BA(G) and BA(H) are isomorphic. As a consequence, we show the existence of non-isomorphic groups G and H such that BA(G) and BA(H) are isomorphic rings. Here, the abelian fiber group A can be chosen in a non-trivial way, that is, such that BA(G) and BA(H) are strictly bigger than the Burnside rings of G and H, for which such counterexamples are already known.Communicated by Mandi Schaeffer Fry

Key concepts: Mathematics, Fibered knot, Counterexample, Abelian group, Pure mathematics, Combinatorics, Group (periodic table), Chemistry

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