The classification of local m-GCI-group on finite nonabelian simple groups

TL;DR

This paper classifies local 2-GCI-groups and 2-GCI-groups within finite nonabelian simple groups, advancing understanding of generalized Cayley graphs and their symmetries.

Contribution

It introduces the concept of local m-GCI-groups for generalized Cayley graphs and provides a classification for local 2-GCI-groups and 2-GCI-groups in simple groups.

Findings

Classification of local 2-GCI-groups achieved

Complete classification of 2-GCI-groups in simple groups

Properties and characterizations of generalized Cayley isomorphisms

Abstract

Li and Praeger classified finite nonabelian simple groups, it has only one or two fusion classes of any certain value. As a by-product, they classified m-CI-groups, which is critical in the research of Cayley graphs. In the paper, we will consider generalized Cayley graphs. This concept is proposed by Marusic et al. In the paper, (local) m- GCI-group is defined, and we get many properties and characterizations based on the generalized Cayley isomorphism, which are the key measures for the classification of (local) m-GCI-group. And above all, we will give a classification of local 2-GCI-groups and 2-GCI-groups for finite nonabelian simple groups.