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

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