Lower bound for the number of conjugacy classes and irreducible characters

被引：1

作者：

Gao, Yinling ^{[1
]}

Yang, Yong ^{[1
,2
]}

机构：

[1] China Three Gorges Univ, Three Gorges Math Res Ctr, Yichang 443002, Hubei, Peoples R China

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

来源：

MONATSHEFTE FUR MATHEMATIK | 2024年 / 203卷 / 02期

关键词：

Finite groups; Odd-degree representations; Characters; Coprime action; ORBITS;

D O I：

10.1007/s00605-023-01860-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give a lower bound for the class number of the semidirect product of an odd-order group acting coprimely on an abelian p-group. For a prime p and a Sylow p-subgroup P of a finite group G, we also obtain an explicit lower bound for the number of p'-degree irreducible characters of G in terms of |P/P'|.

引用

页码：341 / 355

页数：15

共 50 条

[21] Landau's theorem and the number of conjugacy classes of zeros of characters
Moreto, Alexander
[J]. JOURNAL OF ALGEBRA, 2021, 577 : 203 - 209
[22] On the number of conjugacy classes of zeros of characters and the length of solvable groups
Yang, Yong
[J]. COMMUNICATIONS IN ALGEBRA, 2020, 48 (08) : 3590 - 3593
[23] Lower bounds for the number of conjugacy classes of finite groups
Keller, Thomas Michael
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2009, 147 : 567 - 577
[24] Lower bounds for the number of conjugacy classes in finite groups
Bertram, Edward A.
[J]. ISCHIA GROUP THEORY 2004, PROCEEDINGS, 2006, 402 : 95 - 117
[25] Lower bound number of irreducible graphs on surfaces
Liu, Y
Liu, YP
[J]. ACTA MATHEMATICA SCIENTIA, 1998, 18 (03) : 333 - 339
[26] LOWER BOUND NUMBER OF IRREDUCIBLE GRAPHS ON SURMCES
刘莹
刘彦佩
[J]. Acta Mathematica Scientia, 1998, (03) : 333 - 339
[27] SOME CONNECTIONS BETWEEN POWERS OF CONJUGACY CLASSES AND DEGREES OF IRREDUCIBLE CHARACTERS IN SOLVABLE GROUPS
Robati, S. M.
[J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2016, 42 (01) : 19 - 25
[28] The number of conjugacy classes
Reid, M
[J]. AMERICAN MATHEMATICAL MONTHLY, 1998, 105 (04): : 359 - 361
[29] Real-Imaginary Conjugacy Classes and Real-Imaginary Irreducible Characters in Finite Groups
Robati, S. M.
[J]. MATHEMATICAL NOTES, 2018, 103 (1-2) : 251 - 258
[30] Real-Imaginary Conjugacy Classes and Real-Imaginary Irreducible Characters in Finite Groups
S. M. Robati
[J]. Mathematical Notes, 2018, 103 : 251 - 258

← 1 2 3 4 5 →