Third Homology of some Sporadic Finite Groups

TL;DR

This paper calculates the integral third homology groups for most sporadic finite simple groups and their central extensions, providing new algebraic topological insights into these complex structures.

Contribution

It presents the first comprehensive computation of the third homology for a wide class of sporadic groups and their central extensions.

Findings

Computed third homology for most sporadic groups

Determined homology for their central extensions

Enhanced understanding of algebraic topology of sporadic groups

Abstract

We compute the integral third homology of most of the sporadic finite simple groups and of their central extensions.