2020/07/23 by Michael P. Epstein, Epstein, Michael
Computer Science · Mathematics · #20D60 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2007.12208
openalex publication_date 2020/07/23 · openalex created_date 2021/09/27 · openalex updated_date 2026/07/28
A finite cover of a group G is a finite collection C of proper subgroups of G with the property that \bigcup 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 C is a finite cover of a group G, and no cover of G with fewer subgroups exists, then C is said to be a minimal cover of G, and the cardinality of C is called the covering number of G, denoted by σ(G). Here we investigate the covering numbers of the McLaughlin sporadic simple group and some low degree primitive groups.