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Closure Operations On Subgroups, Paige Mankey

Mathematics & Statistics ETDs

During the past five years, a number of mathematicians have conducted research involving closure operations on the ideals of commutative rings. The most accessible paper on this is written by Neil Epstein, entitled "A Guide to Closure Operations in Commutative Algebra". This paper compiles much of the research done on the topic, and gives the reader an overview of closure operations on ideals, and includes examples, methods for constructions, and various special properties that arise from these operations as they pertain to ideals. However, very little research--if any--has been done on closures of subgroups. This thesis aims to give a …