Arithmetic in Group Extensions

TL;DR

This paper introduces a generalized group presentation method tailored for groups with a nontrivial solvable radical, enabling more efficient arithmetic and memory use, demonstrated through the construction of a maximal subgroup of the sporadic monster group and its character table.

Contribution

It presents a new generalized group presentation technique that improves efficiency for groups with solvable radicals, with practical applications in group theory computations.

Findings

Constructed a maximal subgroup of the sporadic monster group

Calculated its previously unknown character table

Demonstrated efficiency improvements in group arithmetic

Abstract

We describe a generalization of the concept of a pc presentation that applies to groups with a nontrivial solvable radical. Such a representation can be much more efficient in terms of memory use and even of arithmetic, than permuattion and matrix representations. We illustrate the use of such representations by constructing a maximal subgroup of the sporadic monster group and calculating its -- hitherto unknown -- character table.