Work

On finite groups with the Magnus Property

Year: 2024

Type: article

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.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.13119

Authors: Martino Garonzi, Claude Marion

Institutions: Universidade de Brasília, Universidade do Porto, Centro de Matemática

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Apoio à Pesquisa do Distrito Federal, Fundação para a Ciência e a Tecnologia

Awards: G2681540997, Centro de Matemática da Universidade do Porto, G466472291, Centro de Matemática da Universidade do Porto