Abstract
For a finite group G denote by N(G) the set of conjugacy class sizes of G. In 1980s, J.G.Thompson posed the following conjecture: If L is a finite nonabelian simple group, G is a finite group with trivial center and N(G) = N(L), then G ≅ L. We prove this conjecture for an infinite class of simple groups. Let p be an odd prime. We show that every finite group G with the property Z(G) = 1 and N(G) = N(A i ) is necessarily isomorphic to A i , where i ∈ {2p, 2p + 1}.
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Babai, A., Mahmoudifar, A. Thompson’s conjecture for the alternating group of degree 2p and 2p+1. Czech Math J 67, 1049–1058 (2017). https://doi.org/10.21136/CMJ.2017.0396-16
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DOI: https://doi.org/10.21136/CMJ.2017.0396-16