The covering number of $M_{24}$

Year 2016, Volume: 3 Issue: 3, 155 - 158, 09.08.2016

Michael Epstein Spyros S. Magliveras

https://doi.org/10.13069/jacodesmath.90728

Abstract

A  finite cover $\mathcal{C}$ of a group $G$ is a finite collection of proper subgroups of $G$ such that $G$ is equal to the union of all of the members of $\mathcal{C}$. Such a cover is called {\em minimal} if it has the smallest cardinality among all finite covers of $G$. The  covering number of $G$, denoted by $\sigma(G)$, is the number of subgroups in a minimal cover of $G$. In this paper the covering number of the Mathieu group $M_{24}$ is shown to be 3336.

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