Blocks of small defect in alternating groups and squares of Brauer character degrees

Xiaoyou Chen; James P. Cossey; Mark L. Lewis; Hung P. Tong-Viet

doi:10.1515/jgth-2017-0025

Blocks of small defect in alternating groups and squares of Brauer character degrees

Xiaoyou Chen
, James P. Cossey
, Mark L. Lewis
, Hung P. Tong-Viet

Mathematics and Statistics

Binghamton University

Henan University of Technology
University of Akron
Kent State University

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

11 Scopus citations

Abstract

Let p be a prime. We show that other than a few exceptions, alternating groups will have p-blocks with small defect for p equal to 2 or 3. Using this result, we prove that a finite group G has a normal Sylow p-subgroup P and G=P is nilpotent if and only if φ(1)² divides |G: ker(φ)| for every irreducible Brauer character φ of G.

Original language	English
Pages (from-to)	1155-1173
Number of pages	19
Journal	Journal of Group Theory
Volume	20
Issue number	6
DOIs	https://doi.org/10.1515/jgth-2017-0025
State	Published - Nov 2017

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title = "Blocks of small defect in alternating groups and squares of Brauer character degrees",

abstract = "Let p be a prime. We show that other than a few exceptions, alternating groups will have p-blocks with small defect for p equal to 2 or 3. Using this result, we prove that a finite group G has a normal Sylow p-subgroup P and G=P is nilpotent if and only if φ(1)2 divides |G: ker(φ)| for every irreducible Brauer character φ of G.",

author = "Xiaoyou Chen and Cossey, \{James P.\} and Lewis, \{Mark L.\} and Tong-Viet, \{Hung P.\}",

note = "Publisher Copyright: {\textcopyright} de Gruyter 2017.",

year = "2017",

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doi = "10.1515/jgth-2017-0025",

language = "English",

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T1 - Blocks of small defect in alternating groups and squares of Brauer character degrees

AU - Chen, Xiaoyou

AU - Cossey, James P.

AU - Lewis, Mark L.

AU - Tong-Viet, Hung P.

PY - 2017/11

Y1 - 2017/11

N2 - Let p be a prime. We show that other than a few exceptions, alternating groups will have p-blocks with small defect for p equal to 2 or 3. Using this result, we prove that a finite group G has a normal Sylow p-subgroup P and G=P is nilpotent if and only if φ(1)2 divides |G: ker(φ)| for every irreducible Brauer character φ of G.

AB - Let p be a prime. We show that other than a few exceptions, alternating groups will have p-blocks with small defect for p equal to 2 or 3. Using this result, we prove that a finite group G has a normal Sylow p-subgroup P and G=P is nilpotent if and only if φ(1)2 divides |G: ker(φ)| for every irreducible Brauer character φ of G.

UR - https://www.scopus.com/pages/publications/85037717310

U2 - 10.1515/jgth-2017-0025

DO - 10.1515/jgth-2017-0025

M3 - Article

SN - 1433-5883

VL - 20

SP - 1155

EP - 1173

JO - Journal of Group Theory

JF - Journal of Group Theory

IS - 6

ER -

Blocks of small defect in alternating groups and squares of Brauer character degrees

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