Character degrees in blocks and defect groups

被引：3

作者：

Giannelli, Eugenio ^{[1
]}

Miquel Martinez, J. ^{[2
]}

Fry, A. A. Schaeffer ^{[3
]}

机构：

[1] Univ Dini, Dipartimento Matemat & Informat, Viale Morgagni 67-A, Florence, Italy

[2] Univ Valencia, Dept Matemat, Burjassot 46100, Spain

[3] Metropolitan State Univ Denver, Dept Math & Stat, Denver, CO 80217 USA

来源：

JOURNAL OF ALGEBRA | 2022年 / 594卷

基金：

美国国家科学基金会;

关键词：

Character degrees; Defect groups; Derived length; P-BLOCKS; FINITE; HEIGHTS; CONJECTURE; LENGTH;

D O I：

10.1016/j.jalgebra.2021.11.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A recent question of Gabriel Navarro asks whether it is true that the derived length of a defect group is less than or equal to the number of degrees of irreducible characters in a block. In this article, we bring new evidence towards the validity of this statement.(c) 2021 Elsevier Inc. All rights reserved.

引用

页码：170 / 193

页数：24

共 44 条

[21] Kurzweil H., 2003, THEORY FINITE GROUPS
[22] Rationality properties of unipotent representations
Lusztig, G
[J]. JOURNAL OF ALGEBRA, 2002, 258 (01) : 1 - 22
[23] Extensions of unipotent characters and the inductive McKay condition
Malle, Gunter
[J]. JOURNAL OF ALGEBRA, 2008, 320 (07) : 2963 - 2980
[24] Brauer's Height Zero Conjecture for principal blocks
Malle, Gunter
Navarro, Gabriel
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2021, 778 : 119 - 125
[25] BLOCKS WITH EQUAL HEIGHT ZERO DEGREES
Malle, Gunter
Navarro, Gabriel
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (12) : 6647 - 6669
[26] The derived length of p-groups
Mann, A
[J]. JOURNAL OF ALGEBRA, 2000, 224 (02) : 263 - 267
[27] Degrees of characters in the principal block
Miquel Martinez, J.
[J]. JOURNAL OF ALGEBRA, 2021, 579 : 195 - 209
[28] Moretó A, 2005, FINITE GROUPS 2003, P267
[29] Navarro G., 1998, CHARACTERS BLOCKS FI
[30] NAVARRO G., 2018, CAMBRIDGE STUDIES AD, V175, DOI DOI 10.1017/9781108552790

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