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The Covering Numbers of Some Finite Simple Groups

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, denoted by σ(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 ≤ 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. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Identiferoai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_41342
ContributorsEpstein, Michael (author), Magliveras, Spyros S. (Thesis advisor), Florida Atlantic University (Degree grantor), Charles E. Schmidt College of Science, Department of Mathematical Sciences
PublisherFlorida Atlantic University
Source SetsFlorida Atlantic University
LanguageEnglish
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation, Text
Format104 p., application/pdf
RightsCopyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder., http://rightsstatements.org/vocab/InC/1.0/

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