Nonsolvable Groups with no Prime Dividing Four Character Degrees

被引：5

作者：

Ghaffarzadeh, Mehdi ^{[1
]}

Ghasemi, Mohsen ^{[2
]}

Lewis, Mark L. ^{[3
]}

Tong-Viet, Hung P. ^{[3
]}

机构：

[1] Islamic Azad Univ, Khoy Branch, Dept Math, Khoy, Iran

[2] Urmia Univ, Dept Math, Orumiyeh 57135, Iran

[3] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2017年 / 20卷 / 03期

关键词：

Character degrees; Prime divisors; SOLVABLE-GROUPS; GRAPHS;

D O I：

10.1007/s10468-016-9654-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a finite group G, we say that G has property if every set of k distinct irreducible character degrees of G is setwise relatively prime. In this paper, we show that if G is a finite nonsolvable group satisfying then G has at most 8 distinct character degrees. Combining with work of D. Benjamin on finite solvable groups, we deduce that a finite group G has at most 9 distinct character degrees if G has property and this bound is sharp.

引用

页码：547 / 567

页数：21

共 50 条

[1] Nonsolvable Groups with no Prime Dividing Four Character Degrees
Mehdi Ghaffarzadeh
Mohsen Ghasemi
Mark L. Lewis
Hung P. Tong-Viet
Algebras and Representation Theory, 2017, 20 : 547 - 567
[2] Nonsolvable groups with no prime dividing three character degrees
Lewis, Mark L.
White, Donald L.
JOURNAL OF ALGEBRA, 2011, 336 (01) : 158 - 183
[3] On the multiplicity of character degrees of nonsolvable groups
Sayanjali, Z.
Akhlaghi, Z.
Khosravi, B.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2021, 20 (05)
[4] FINITE NONSOLVABLE GROUPS WITH MANY DISTINCT CHARACTER DEGREES
Tong-Viet, Hung P.
PACIFIC JOURNAL OF MATHEMATICS, 2014, 268 (02) : 477 - 492
[5] GROUPS WITH FOUR CHARACTER DEGREES AND DERIVED LENGTH FOUR
Du, Ni
Lewis, Mark L.
COMMUNICATIONS IN ALGEBRA, 2015, 43 (11) : 4660 - 4673
[6] NONSOLVABLE GROUPS ALL OF WHOSE CHARACTER DEGREES ARE ODD-SQUARE-FREE
Lewis, Mark L.
White, Donald L.
COMMUNICATIONS IN ALGEBRA, 2011, 39 (04) : 1273 - 1292
[7] Constructing solvable groups with derived length four and four character degrees
Lewis, Mark L.
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2019, 94 (3-4): : 395 - 407
[8] Nonsolvable groups satisfying the prime-power hypothesis
Liu, Yanjun
Song, Xueling
Zhang, Jiping
JOURNAL OF ALGEBRA, 2015, 442 : 455 - 483
[9] Fitting heights of solvable groups with no nontrivial prime power character degrees
Lewis, Mark L.
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2017, 90 (3-4): : 311 - 317
[10] PRIME DIVISORS OF IRREDUCIBLE CHARACTER DEGREES
Tong-Viet, Hung P.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2015, 45 (05) : 1645 - 1658

← 1 2 3 4 5 →