Thompson’s conjecture for the alternating group of degree 2p and 2p+1

چکیده مقاله

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}. © 2017, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.