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

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.

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

scholarly journals On bipartite divisor graphs for group conjugacy class sizes

2009 ◽  
Vol 213 (9) ◽  
pp. 1722-1734 ◽  
Author(s):  
Daniela Bubboloni ◽  
Silvio Dolfi ◽  
Mohammad A. Iranmanesh ◽  
Cheryl E. Praeger
Keyword(s):  
Conjugacy Class ◽  
Conjugacy Class Sizes

On the normal subgroup with coprime G-conjugacy class sizes

2011 ◽  
Vol 121 (4) ◽  
pp. 397-404 ◽  
Author(s):  
XIANHE ZHAO ◽  
GUIYUN CHEN ◽  
JIAOYUN SHI
Keyword(s):  
Normal Subgroup ◽  
Conjugacy Class ◽  
Conjugacy Class Sizes
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