Counting the number of automorphisms of finite abelian groups

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Authors
Krause, Linda J.
Advisor
Bremigan, Ralph J.
Issue Date
1994
Keyword
Degree
Thesis (M.S.)
Department
Department of Mathematical Sciences
Other Identifiers
Abstract

The purpose of this paper was to find a general formula to count the number of automorphisms of any finite abelian group. These groups were separated into five different types. For each of the first three types, theorems were proven, and formulas were derived based on the theorems. A formula for the last two types of groups was derived from a theorem based on a conjecture which was proven in only one direction. Then it was shown that a count found from any of the first three formulas could also be found using the last formula. The result of these comparisons gave credence to the conjecture. Thus we found that the last formula is a general formula to count the number of automorphisms of finite abelian groups.

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