GROUPS WITH FEW CONJUGACY CLASSES

被引：7

作者：

Hethelyi, Laszlo ^{[1
]}

Horvath, Erzsebet ^{[1
]}

Keller, Thomas Michael ^{[2
]}

Maroti, Attila ^{[3
]}

机构：

[1] Budapest Univ Technol & Econ, Inst Math, Dept Algebra, H-1521 Budapest, Hungary

[2] Texas State Univ, Dept Math, San Marcos, TX 78666 USA

[3] MTA Alfred Renyi Inst Math, H-1053 Budapest, Hungary

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2011年 / 54卷

关键词：

finite group; conjugacy classes; lower bound; Frobenius group; FINITE-GROUPS; NUMBER; CLASSIFICATION;

D O I：

10.1017/S001309150900176X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group, let p be a prime divisor of the order of G and let k(G) be the number of conjugacy classes of G. By disregarding at most finitely many non-solvable p-solvable groups G, we have k(G) >= 2 root p - 1 with equality if and only if root p - 1 is an integer, G = C(p) x C root p - 1 and C(G)(C(p)) = C(p). This extends earlier work of Hethelyi, Kulshammer, Malle and Keller.

引用

页码：423 / 430

页数：8

共 50 条

[21] Groups with bounded verbal conjugacy classes
Brazil, S
Krasilnikov, A
Shumyatsky, P
JOURNAL OF GROUP THEORY, 2006, 9 (01) : 127 - 137
[22] Conjugacy classes of centralizers in unitary groups
Bhunia, Sushil
Singh, Anupam
JOURNAL OF GROUP THEORY, 2019, 22 (02) : 231 - 251
[23] Conjugacy classes in integral symplectic groups
Yang, Qingjie
LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 418 (2-3) : 614 - 624
[24] Conjugacy classes in Möbius groups
Krishnendu Gongopadhyay
Geometriae Dedicata, 2011, 151 : 245 - 258
[25] ON GRAPHS RELATED TO CONJUGACY CLASSES OF GROUPS
ALFANDARY, G
ISRAEL JOURNAL OF MATHEMATICS, 1994, 86 (1-3) : 211 - 220
[26] CONJUGACY CLASSES AND REPRESENTATION-GROUPS
NOBUSAWA, N
OSAKA JOURNAL OF MATHEMATICS, 1990, 27 (01) : 223 - 228
[27] Linear Groups with Restricted Conjugacy Classes
F. de Giovanni
M. Trombetti
B. A. F. Wehrfritz
Ricerche di Matematica, 2022, 71 : 179 - 188
[28] Twisted Conjugacy Classes in Chevalley Groups
T. R. Nasybullov
Algebra and Logic, 2015, 53 : 481 - 501
[29] On the computation of conjugacy classes of chevalley groups
Fleischmann, P
Janiszczak, I
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 1996, 7 (03) : 221 - 234
[30] Statistics in conjugacy classes in free groups
Kenison, George
Sharp, Richard
GEOMETRIAE DEDICATA, 2019, 198 (01) : 57 - 70

← 1 2 3 4 5 →