π-Height Zero Characters in the Principal π-Block and π-Nilpotence of a π-Separable Group

• 来源期刊: 代数集刊（英文版）
• 关键词: principal π-block π-height π-weight π-nilpotent
• 年，卷（期）: 2003,（3）
• 页码范围: 267-273
• 页数: 7页
• 语种: 英文

摘要

Murai [6] obtained some important connections between height zero characters in the principal p-block and p-nilpotence of a finite group. In this paper, we generalize Murai's results to the π-block theory in a π-separable group,and prove that if π-Hall subgroups are nilpotent, then the intersection of kernels of π-height zero characters in the principal π-block is π-nilpotent; and then G is π-nilpotent if and only if π-height zero characters in the principal π-block are linear.Also, we obtain an equivalent condition for G being π-nilpotent by π-weights of G.