Recognition of \(A_1\)\(_0\) and \(L_4\)(4) by two special conjugacy class sizes - Chen, Yanheng; Chen, Guiyun (Italian Journal of Pure and Applied Mathematics, 2012)
It is well-known that A10 is the smallest (by order) nonabelian simple group with connected prime graph and L4(4) is the smallest nonabelian simple group of Lie type with connected prime graph. In 2009, A.V. Vasil'ev first dealt with the groups with connected prime graph and proved that Thompson's conjecture holds for A10 and L4(4) (see [1]). In this work, the authors characterize finite simple groups A10 and L4(4) by their orders and largest and smallest conjugacy class sizes greater than 1, and partially generalize A.V. Vasil'ev's work.