Math Department (Thesis/2009-10)

Groups as Unions of Proper Subgroups

Under the direction of: Paul Friedman

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This month's issue of ''The American Mathematical Monthly'' (known as The Monthly) has a very interesting article entitled ''Groups as Unions of Proper Subgroups,'' by Mira Bhargava. The introduction of the article is

''The following question has been asked many times and also appeared as a problem on the 1965 William Lowell Putnam Exam: When is a group the union of two proper subgroups?

''The answer, as is now well known, is:

'' Theorem 1. A group is never the union of two proper subgroups.

''$\ldots$ There are several natural variants of the above question, however, that have positive and, in many cases, very pretty and surprising answers.''

This thesis would read this paper, study the question, theorem, and its variants.

This is a two-term thesis. Prerequisite: Math 332.

Math Department web pages Created: 11 May 2009 Last modified: May 11, 2009 10:26:36 AM Comments to: math@union.edu

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