Corrigendum on the solvability of groups with four class sizes

Abstract

The authors have realized that in the proof of Theorem 6 of [1] there is a mistake although the conclusion of the theorem is correct. The proof of the theorem is divided into two cases: when there exist no p-elements of index pa in the group G and when there exist. In the second case of the proof, the authors apply Lemma 4 of [1] to the abelian normal subgroup Op (G). However, the conclusion is false, so the final contradiction is not achieved as it is argued in the paper. In order to solve this, we provide here a correction of this case