The covering numbers of the McLaughlin group and some primitive groups of low degree
DOI:
https://doi.org/10.13069/jacodesmath.v9i3.172Keywords:
Covering numbers, McLaughlin group, Primitive groupsAbstract
A \emph{finite cover} of a group $G$ is a finite collection $\mathcal{C}$ of proper subgroups of $G$ with the property that $\bigcup \mathcal{C} = G$. A finite group admits a finite cover if and only if it is noncyclic. More generally, it is known that a group admits a finite cover if and only if it has a finite, noncyclic homomorphic image. If $\mathcal{C}$ is a finite cover of a group $G$, and no cover of $G$ with fewer subgroups exists, then $\mathcal{C}$ is said to be a \emph{minimal cover} of $G$, and the cardinality of $\mathcal{C}$ is called the \emph{covering number} of $G$, denoted by $\sigma(G)$. Here we investigate the covering numbers of the McLaughlin sporadic simple group and some low degree primitive groups.
Received: 7 November 2020 | Accepted: 21 March 2022
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