2-parts of real class sizes

Hung P. Tong-Viet

doi:10.2140/ant.2018.12.2499

2-parts of real class sizes

Hung P. Tong-Viet

Mathematics and Statistics

Binghamton University

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

Abstract

We investigate the structure of finite groups whose noncentral real class sizes have the same 2-part. In particular, we prove that such groups are solvable and have 2-length one. As a consequence, we show that a finite group is solvable if it has two real class sizes. This confirms a conjecture due to G. Navarro, L. Sanus and P. Tiep.

Original language	English
Pages (from-to)	2499-2514
Number of pages	16
Journal	Algebra and Number Theory
Volume	12
Issue number	10
DOIs	https://doi.org/10.2140/ant.2018.12.2499
State	Published - 2018

Keywords

2-parts
Involutions
Quasisimple groups
Real conjugacy classes

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10.2140/ant.2018.12.2499

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title = "2-parts of real class sizes",

abstract = "We investigate the structure of finite groups whose noncentral real class sizes have the same 2-part. In particular, we prove that such groups are solvable and have 2-length one. As a consequence, we show that a finite group is solvable if it has two real class sizes. This confirms a conjecture due to G. Navarro, L. Sanus and P. Tiep.",

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TY - JOUR

T1 - 2-parts of real class sizes

AU - Tong-Viet, Hung P.

PY - 2018

Y1 - 2018

N2 - We investigate the structure of finite groups whose noncentral real class sizes have the same 2-part. In particular, we prove that such groups are solvable and have 2-length one. As a consequence, we show that a finite group is solvable if it has two real class sizes. This confirms a conjecture due to G. Navarro, L. Sanus and P. Tiep.

AB - We investigate the structure of finite groups whose noncentral real class sizes have the same 2-part. In particular, we prove that such groups are solvable and have 2-length one. As a consequence, we show that a finite group is solvable if it has two real class sizes. This confirms a conjecture due to G. Navarro, L. Sanus and P. Tiep.

KW - 2-parts

KW - Involutions

KW - Quasisimple groups

KW - Real conjugacy classes

UR - https://www.scopus.com/pages/publications/85062676807

U2 - 10.2140/ant.2018.12.2499

DO - 10.2140/ant.2018.12.2499

M3 - Article

SN - 1937-0652

VL - 12

SP - 2499

EP - 2514

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 10

ER -

2-parts of real class sizes

Abstract

Keywords

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