On the non-existence of finite groups with certain normal subgroups

Abstract

Problem 20.21 of Mazurov and Khukhro (Unsolved Problems in Group Theory: The Kourovka Notebook, 20th Issue, 2022), contributed by M.~Conder and attributed to G.~Verret, asks whether there exists a finite group $G$ with two normal subgroups $K$ and $L$ of index $12$ such that $K\cong L$, but with non-isomorphic quotients $G/K\cong C_{12}$ and $G/L\cong A_4.$ We prove that no such finite group exists.

arXiv commentWe have discovered an error in Section 3.4 that affects the main arguments, and we wish to withdraw the paper until it can be corrected