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2014•Bulletin of the London Mathematical SocietyRequires access

Finite groups with two conjugacy classes ofp-elements and related questions forp-blocks

Burkhard Külshammer, Gabriel Navarro, Benjamin Sambale, Pham Huu Tiep

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Abstract

We prove that a finite group in which any two nontrivial p-elements are conjugate have Sylow p-subgroups which are either elementary abelian or extra-special of order p 3 and exponent p.

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What this paper is about

We prove that a finite group in which any two nontrivial p-elements are conjugate have Sylow p-subgroups which are either elementary abelian or extra-special of order p 3 and exponent p.

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OpenAlex reports 19 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We prove that a finite group in which any two nontrivial p-elements are conjugate have Sylow p-subgroups which are either elementary abelian or extra-special of order p 3 and exponent p.

Key concepts: Sylow theorems, Conjugacy class, Mathematics, Abelian group, Locally finite group, Exponent, Order (exchange), p-group

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