Prime Factors of π-Partial Character Degrees and Conjugacy Class Sizes of π-Elements

• 来源期刊: 代数集刊（英文版）
• 关键词: finite groups conjugacy classes character degrees
• 年，卷（期）: 2005,（4）
• 页码范围: 699-707
• 页数: 9页
• 语种: 英文

摘要

Let G be a finite solvable group. We prove that any prime dividing any irreducible π-partial character degree of G divides the size of some conjugacy class of π-elements of G. Under certain hypothesis, we show that if two distinct primes r and s both divide some irreducible π-partial character degree, then there exists a conjugacy class of π-elements whose size is divisible by rs.