Normal Sylow subgroups and monomial Brauer characters

2021 ◽  
Author(s):  
Xiaoyou Chen ◽  
Long Miao
Keyword(s):  
Sylow Subgroups ◽  
Brauer Characters

DEGREES OF BRAUER CHARACTERS AND NORMAL SYLOW -SUBGROUPS

2020 ◽  
Vol 102 (2) ◽  
pp. 237-239
Author(s):  
XIAOYOU CHEN ◽  
MARK L. LEWIS
Keyword(s):  
Solvable Group ◽  
Sylow Subgroups ◽  
Brauer Characters

Let $p$ be a prime, $G$ a solvable group and $P$ a Sylow $p$-subgroup of $G$. We prove that $P$ is normal in $G$ if and only if $\unicode[STIX]{x1D711}(1)_{p}^{2}$ divides $|G:\ker (\unicode[STIX]{x1D711})|_{p}$ for all monomial monolithic irreducible $p$-Brauer characters $\unicode[STIX]{x1D711}$ of $G$.

The complements in an affine group

2013 ◽  
Vol 50 (2) ◽  
pp. 258-265
Author(s):  
Pál Hegedűs
Keyword(s):  
Permutation Group ◽  
Structural Similarity ◽  
Affine Group ◽  
Permutation Module ◽  
Regular Module ◽  
Brauer Characters

In this paper we analyse the natural permutation module of an affine permutation group. For this the regular module of an elementary Abelian p-group is described in detail. We consider the inequivalent permutation modules coming from nonconjugate complements. We prove their strong structural similarity well exceeding the fact that they have equal Brauer characters.

scholarly journals Low-dimensional representations of finite orthogonal groups

2021 ◽  
pp. 1-22
Author(s):  
KAY MAGAARD ◽  
GUNTER MALLE
Keyword(s):  
Orthogonal Groups ◽  
Brauer Characters ◽  
Low Dimensional

Abstract We determine the smallest irreducible Brauer characters for finite quasi-simple orthogonal type groups in non-defining characteristic. Under some restrictions on the characteristic we also prove a gap result showing that the next larger irreducible Brauer characters have a degree roughly the square of those of the smallest non-trivial characters.

Brauer characters and fields of values

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Dan Rossi
Keyword(s):  
Prime Number ◽  
Brauer Characters

AbstractFor a prime number

scholarly journals The Sylow subgroups of the absolute Galois group Gal(Q)

2015 ◽  
Vol 284 ◽  
pp. 186-212 ◽  
Author(s):  
Lior Bary-Soroker ◽  
Moshe Jarden ◽  
Danny Neftin
Keyword(s):  
Galois Group ◽  
Absolute Galois Group ◽  
Sylow Subgroups ◽  
The Absolute

scholarly journals ON A CLASS OF SUPERSOLUBLE GROUPS

2014 ◽  
Vol 90 (2) ◽  
pp. 220-226 ◽  
Author(s):  
A. BALLESTER-BOLINCHES ◽  
J. C. BEIDLEMAN ◽  
R. ESTEBAN-ROMERO ◽  
M. F. RAGLAND
Keyword(s):  
Finite Group ◽  
Maximal Subgroups ◽  
Supersoluble Groups ◽  
Sylow Subgroups ◽  
A Finite Group

AbstractA subgroup $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H$ of a finite group $G$ is said to be S-semipermutable in $G$ if $H$ permutes with every Sylow $q$-subgroup of $G$ for all primes $q$ not dividing $|H |$. A finite group $G$ is an MS-group if the maximal subgroups of all the Sylow subgroups of $G$ are S-semipermutable in $G$. The aim of the present paper is to characterise the finite MS-groups.

scholarly journals On CSQ-normal subgroups of finite groups

2016 ◽  
Vol 14 (1) ◽  
pp. 801-806
Author(s):  
Yong Xu ◽  
Xianhua Li
Keyword(s):  
Finite Groups ◽  
Normal Subgroups ◽  
Sylow Subgroups

Abstract We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.

scholarly journals Nonabelian Sylow subgroups of finite groups of even order

1998 ◽  
Vol 4 (12) ◽  
pp. 88-90
Author(s):  
Naoki Chigira ◽  
Nobuo Iiyori ◽  
Hiroyoshi Yamaki
Keyword(s):  
Finite Groups ◽  
Sylow Subgroups ◽  
Even Order

scholarly journals Strong duality for metacyclic groups

2002 ◽  
Vol 73 (3) ◽  
pp. 377-392 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó
Keyword(s):  
Finite Group ◽  
Dihedral Group ◽  
Strong Duality ◽  
Sylow Subgroups ◽  
Metacyclic Groups ◽  
Group D

AbstractDavey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).

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