Solving the Class Equation x<sup>d</sup>= β in an Alternating Group for Each β ∈ C<sup>α</sup>∩ H<sub>n</sub><sup>c</sup>and n >1

• 作者: Andrew Rajah Shuker Mahmood
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: Alternating Groups PERMUTATIONS Conjugate Classes Cycle Type FROBENIUS Equation
• 年，卷（期）: 2012,（2）
• 页码范围: 13-19
• 页数: 7页
• 分类号: O1

摘要

The main purpose of this paper is to solve the class equation in an alternating group, (i.e. find the solutions set ) and find the number of these solutions where ranges over the conjugacy class in and d is a positive integer. In this paper we solve the class equation in where , for all . is the complement set of where { of , with all parts of are different and odd}. is conjugacy class of and form class depends on the cycle type of its elements If and , then splits into the two classes of .