Combinatorial method in the coset enumeration of symmetrically generated groups

Abstract

Several finite groups, including all non-abelian finite simple groups, can be generated by finite conjugacy classes of involutions. We describe a coset enumeration algorithm that is particularly developed for a group defined in this manner. We illustrate the process by using some rather small examples for which the enumerations can be worked manually.

Keywords:

• coset enumerations
• symmetric generations
• involutory generators
• combinatorial algebra
• enumetration

2000 AMS Subject Classification :

• 05A05
• 20B05
• 20B40

CCS Category :

• I.1.2