不可约特征的协度的p部分

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2021-03-01 DOI:10.5802/CRMATH.158

Roya Bahramian, N. Ahanjideh

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引用次数: 5

摘要

对于有限群G的一个特征χ， χ的共度为χc (1) = [G:kerχ] χ(1)。设p为质数，e为正整数。本文首先证明了如果G是p可解群，使得对于G的每一个不可约字符χ， p +1 χc(1)，则G的p长度不大于e。然后研究了满足p2不除其不可约字符的协度的条件的有限群。数学学科分类(2010)。20c15, 20d10, 20d05。稿件于2020年4月22日收稿，于2020年11月24日修订并接受。

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p-parts of co-degrees of irreducible characters

For a character χ of a finite group G , the co-degree of χ is χc (1) = [G :kerχ] χ(1) . Let p be a prime and let e be a positive integer. In this paper, we first show that if G is a p-solvable group such that pe+1 χc (1), for every irreducible character χ of G , then the p-length of G is not greater than e. Next, we study the finite groups satisfying the condition that p2 does not divide the co-degrees of their irreducible characters. Mathematical subject classification (2010). 20C15, 20D10, 20D05. Manuscript received 22nd April 2020, revised and accepted 24th November 2020.

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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.