Corrigendum: Some class sizes conditions implying solvability of finite groups

Abstract

[EN] The authors have realized that the proof of Step 1 in [1, Theorem A] is incomplete. Precisely, in the proof of Step 1 we suppose that there exists a p-element x of index m where p is the set of primes dividing m and we have the following situation: CGðxÞ is a direct product of a p-subgroup and a p0 -subgroup and the class sizes of such p0 -subgroup are at most two numbers: 1 or n. However, the case in which all of them are exactly equal to 1, that is, when the p0 -subgroup is abelian, is omitted and this is the case we complete here by showing that it cannot happen.