Groups of order at most 6 000 generated by two elements, one of which is an involution, and related structures

TL;DR

This paper presents a comprehensive enumeration of (2,*)-groups of order up to 6,000, revealing connections to well-known combinatorial structures and providing valuable data for group theory research.

Contribution

The authors developed a method to generate a complete census of (2,*)-groups of order at most 6,000, including related combinatorial structures, which was not previously available.

Findings

Census of all (2,*)-groups up to order 6,000

Identification of related combinatorial structures

New data for group theory and combinatorics

Abstract

A (2,*)-group is a group that can be generated by two elements, one of which is an involution. We describe the method we have used to produce a census of all (2,*)-groups of order at most 6 000. Various well-known combinatorial structures are closely related to (2,*)-groups and we also obtain censuses of these as a corollary.