Abstract.
We prove that for some families of finite groups, the isomorphism class of the group is completely determined by its Burnside ring. Namely, we prove the following: if two finite simple groups have isomorphic Burnside rings, then the groups are isomorphic; if G is either Hamiltonian or abelian or a minimal simple group, and G′ is any finite group such that B(G) ≅ B(G′), then G ≅ G′.
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Received: 22 April 2004
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Raggi-Cárdenas, A.G., Valero-Elizondo, L. Groups with isomorphic Burnside rings. Arch. Math. 84, 193–197 (2005). https://doi.org/10.1007/s00013-004-1124-x
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DOI: https://doi.org/10.1007/s00013-004-1124-x