Combinatorial methods for determining subgroup structures of finite groups

Abstract

In this paper we discuss methods that might be employed in determining the subgroup structure of a finite group G. These methods have a particularly combinatorial flavor connected with graphs, designs and the combinatorial nature of presentations of groups. In particular, the methods are illustrated for the case of the simple group U_3(5) = PSU_3(5^2) whose maximal subgroups are determined up to conjugacy.

Keywords

• finite groups
• subgroup structure
• combinatorial methods