Dissertation/Thesis Abstract

The Covering Numbers of Some Finite Simple Groups
by Epstein, Michael, Ph.D., Florida Atlantic University, 2019, 105; 13857989
Abstract (Summary)

A finite cover 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 C. Such a cover is called minimal if it has the smallest cardinality among all finite covers of G. The covering number of G is the number of subgroups in a minimal cover of G. Here we determine the covering numbers of the projective special unitary groups U3(q) for q less than or equal to 5, and give upper and lower bounds for the covering number of U3(q) when q > 5. We also determine the covering number of the McLaughlin sporadic simple group, and verify previously known results on the covering numbers of the Higman-Sims and Held groups.

Indexing (document details)
Advisor: Magliveras, Spyros S.
Commitee: Kalva, Hari, Klingler, Lee, Richman, Fred
School: Florida Atlantic University
Department: Mathematics
School Location: United States -- Florida
Source: DAI-B 80/11(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics
Keywords: Finite simple groups, Group covering numbers
Publication Number: 13857989
ISBN: 978-1-392-27457-6
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