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arXiv · 2310.19575

On finite groups with the Magnus Property

Martino Garonzi·Claude Marion
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Abstract

We investigate finite groups with the Magnus Property, where a group is said to have the Magnus Property (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.

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Martino Garonzi, Claude Marion. 2023-10-30. On finite groups with the Magnus Property. https://arxiv.org/abs/2310.19575

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