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.
Fields of Study & Subjects
Finite Group Theory Research
Geometric and Algebraic Topology
Advanced Operator Algebra Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 3 January 2026
- Document type
- Preprint