2024/07/09 by Martino Garonzi, Claude Marion · 2 citations
Mathematics · #Advanced Topics in Algebra #Epistemology #Finite Group Theory Research #Geometric and Algebraic Topology #Mathematics #Philosophy #Property (philosophy) #Pure mathematics
paper · doi:10.1112/blms.13119
openalex publication_date 2024/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Abstract We investigate finite groups with the Magnus Property (MP), where a group is said to have the MP if whenever two elements have the same normal closure, then they are conjugate or inverse conjugate. In particular, we observe that a finite MP group is solvable, determine the finite primitive MP groups, and determine all the possible orders of the chief factors of a finite MP group. We also determine the MP finite direct products of finite primitive groups, as well as the MP crown‐based powers of a finite monolithic primitive group.