An algorithm for finding minimal generating sets of finite groups

Author(s):

Tanakorn Udomworarat , Teerapong Suksumran*

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

In this article, we study connections between components of the Cayley graph Cay(G,A), where A is an arbitrary subset of a group G, and cosets of the subgroup of G generated by A. In particular, we show how to construct generating sets of G if Cay(G,A) has finitely many components. Furthermore, we provide an algorithm for finding minimal generating sets of finite groups using their Cayley graphs.

Keywords:

Cayley graph , Connected graph , Coset , Generating set , Graph component

Language:
English
Published:
Journal of Algebraic Structures and Their Applications, Volume:8 Issue: 2, Summer-Autumn 2021
Pages:
131 to 143
https://www.magiran.com/p2305743