Abstract
Let G be a non-abelian group and N(G) be the set of conjugacy class sizes of G. In 1980s, Thompson posed the following conjecture: if M is a finite non-abelian simple group, G is a finite group with Z(G) = 1 and N(G) = N(M), then M ≅ G. Here, we prove Thompson's conjecture holds for all almost sporadic simple groups.
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