Thompson's conjecture for simple groups with connected prime graph.
Question 12.38 in The Kourovka notebook [2010; Zbl 1211.20001] states that: Let \(N(G)\) denote the set of all orders of the conjugacy class sizes in a finite group \(G\). Is it true that if \(G\) is a finite nonabelian simple group, \(H\) a finite group with trivial centre and \(N(G)=N(H)\) then \(G\) and \(H\) are isomorphic? This question is known as the Thompson conjecture. In the paper under review the author considers finite nonabelian simple groups \(G\) where the prime divisors of the order of \(G\) are numbers in the set \(S=\{2,3,5,7,11,13,17\}\), and verifies Thompson's conjecture for these groups. Although the conjecture was already verified for some of these groups, but the present paper completes the conjecture for finite nonabelian simple groups with order divisible by primes in \(S\).
scientific article; zbMATH DE number 6115027
scientific article