Simplicity of normal subgroups and conjugacy class sizes

2014 ◽  
Vol 175 (4) ◽  
pp. 485-490
Author(s):  
Antonio Beltrán ◽  
María José Felipe
Keyword(s):  
Conjugacy Class ◽  
Normal Subgroups ◽  
Conjugacy Class Sizes

On normal subgroups with consecutive G-class sizes

2016 ◽  
Vol 15 (08) ◽  
pp. 1650151
Author(s):  
Changguo Shao ◽  
Qinhui Jiang
Keyword(s):  
Group Theory ◽  
Normal Subgroup ◽  
Conjugacy Class ◽  
Frobenius Group ◽  
Normal Subgroups ◽  
Conjugacy Class Sizes ◽  
Abelian Kernel ◽  
Consecutive Integers ◽  
Normal Formula

Let [Formula: see text] be a group and [Formula: see text] be a normal subgroup of [Formula: see text]. If the set [Formula: see text] is composed by consecutive integers, then [Formula: see text] is either nilpotent or a quasi-Frobenius group with abelian kernel and complements. This is a generalization of Theorem 2 of [A. Beltrán, M. J. Felipe and C. G. Shao, [Formula: see text]-divisibility of conjugacy class sizes and normal [Formula: see text]-complements, J. Group Theory 18 (2015) 133–141].

A note on class sizes of vanishing elements in finite groups

2021 ◽  
pp. 2250067
Author(s):  
Qingjun Kong ◽  
Shi Chen
Keyword(s):  
Finite Group ◽  
Conjugacy Class ◽  
Finite Groups ◽  
Prime Power ◽  
Prime Power Order ◽  
Normal Subgroups ◽  
Conjugacy Class Sizes ◽  
Vanishing Elements ◽  
A Finite Group

Let [Formula: see text] and [Formula: see text] be normal subgroups of a finite group [Formula: see text]. We obtain th supersolvability of a factorized group [Formula: see text], given that the conjugacy class sizes of vanishing elements of prime-power order in [Formula: see text] and [Formula: see text] are square-free.

Prime Divisors ofp-regular Conjugacy Class Sizes

2015 ◽  
Vol 43 (8) ◽  
pp. 3365-3371 ◽  
Author(s):  
Yang Liu ◽  
Ziqun Lu
Keyword(s):  
Conjugacy Class ◽  
Conjugacy Class Sizes ◽  
Prime Divisors

Numbers Of Conjugacy Class Sizes And Derived Lengths for A-Groups

1996 ◽  
Vol 39 (3) ◽  
pp. 346-351 ◽  
Author(s):  
Mary K. Marshall
Keyword(s):  
Conjugacy Class ◽  
Solvable Group ◽  
Conjugacy Classes ◽  
Finite Solvable Group ◽  
Conjugacy Class Sizes ◽  
Sylow Subgroups ◽  
Derived Length ◽  
Completely Reducible

AbstractAn A-group is a finite solvable group all of whose Sylow subgroups are abelian. In this paper, we are interested in bounding the derived length of an A-group G as a function of the number of distinct sizes of the conjugacy classes of G. Although we do not find a specific bound of this type, we do prove that such a bound exists. We also prove that if G is an A-group with a faithful and completely reducible G-module V, then the derived length of G is bounded by a function of the number of distinct orbit sizes under the action of G on V.

CONJUGACY CLASS SIZES FOR SOME 2-GROUPS OF NILPOTENCY CLASS TWO

2012 ◽  
Vol 57 (1) ◽  
Author(s):  
SHEILA ILANGOVAN ◽  
NOR HANIZA SARMIN
Keyword(s):  
Conjugacy Class ◽  
Nilpotency Class ◽  
Conjugacy Class Sizes

Dalam kertas ini, kita menyelidik ciri tak terturunkan dan panjang kelas konjugat bagi kumpulan–2 berpenjana–2 dengan kelas nilpoten 2. Panjang kelas konjugat bagi elemen x dalam kumpulan G adalah peringkat xG di mana xG ialah kelas konjugat yang mengandungi x. Kajian ini adalah berdasarkan pada klasifikasi kumpulan yang diberikan oleh Magidin pada tahun 2006. Kita akan membuktikan bahawa panjang kelas konjugat bagi G ialah 2ρ di mana 0 <= ρ <= γdan |G'| = 2γ.

scholarly journals A dual version of Huppert's conjecture on conjugacy class sizes

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Zeinab Akhlaghi ◽  
Maryam Khatami ◽  
Tung Le ◽  
Jamshid Moori ◽  
Hung P. Tong-Viet
Keyword(s):  
Conjugacy Class ◽  
Conjugacy Class Sizes ◽  
Dual Version

AbstractIn [J. Algebra 344 (2011), 205–228], a conjecture of J. G. Thompson for PSL

On Conjugacy Class Sizes of the p′-Elements with Prime Power Order

2009 ◽  
Vol 16 (04) ◽  
pp. 541-548 ◽  
Author(s):  
Xianhe Zhao ◽  
Xiuyun Guo
Keyword(s):  
Conjugacy Class ◽  
Solvable Group ◽  
Class Size ◽  
Prime Power ◽  
Prime Power Order ◽  
Conjugacy Class Sizes ◽  
Fixed Integer ◽  
P Elements ◽  
Conjugacy Class Size

In this paper we prove that a finite p-solvable group G is solvable if its every conjugacy class size of p′-elements with prime power order equals either 1 or m for a fixed integer m. In particular, G is 2-nilpotent if 4 does not divide every conjugacy class size of 2′-elements with prime power order.

Conjugacy class sizes and solvability of finite groups

2013 ◽  
Vol 123 (2) ◽  
pp. 239-244 ◽  
Author(s):  
QINHUI JIANG ◽  
CHANGGUO SHAO
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Conjugacy Class Sizes
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