Finite groups with two conjugacy classes of p-elements and related questions for p-blocks

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

doi:10.1112/blms/bdt099

Finite groups with two conjugacy classes of p-elements and related questions for p-blocks

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

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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 p³ and exponent p.

Original language	English (US)
Pages (from-to)	305-314
Number of pages	10
Journal	Bulletin of the London Mathematical Society
Volume	46
Issue number	2
DOIs	https://doi.org/10.1112/blms/bdt099
State	Published - Apr 2014

ASJC Scopus subject areas

General Mathematics

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10.1112/blms/bdt099

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title = "Finite groups with two conjugacy classes of p-elements and related questions for p-blocks",

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 p3 and exponent p.",

author = "Burkhard K{\"u}lshammer and Benjamin Sambale and Gabriel Navarro and Tiep, \{Pham Huu\}",

note = "Funding Information: The research of the second author was supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2010-15296. The third author gratefully acknowledges support through a grant by the Carl Zeiss Foundation. The fourth author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374).",

year = "2014",

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doi = "10.1112/blms/bdt099",

language = "English (US)",

volume = "46",

pages = "305--314",

journal = "Bulletin of the London Mathematical Society",

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T1 - Finite groups with two conjugacy classes of p-elements and related questions for p-blocks

AU - Külshammer, Burkhard

AU - Sambale, Benjamin

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

N1 - Funding Information: The research of the second author was supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2010-15296. The third author gratefully acknowledges support through a grant by the Carl Zeiss Foundation. The fourth author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374).

PY - 2014/4

Y1 - 2014/4

N2 - 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 p3 and exponent p.

AB - 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 p3 and exponent p.

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UR - https://www.scopus.com/pages/publications/84897002156#tab=citedBy

U2 - 10.1112/blms/bdt099

DO - 10.1112/blms/bdt099

M3 - Article

AN - SCOPUS:84897002156

SN - 0024-6093

VL - 46

SP - 305

EP - 314

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 2

ER -

Finite groups with two conjugacy classes of p-elements and related questions for p-blocks

Abstract

ASJC Scopus subject areas

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