Title

An Analog for a Basis in Finite Groups

Document Type

Thesis

Publication Date

2010

Advisor

Bret Benesh, Mathematics

Abstract

I have defined a concept analogous to a basis in a vector space which represents elements in finite groups. Called a group basis, this concept retains properties similar to those of bases in vector spaces, such as span and linear independence. Unlike bases in vector spaces, not all finite groups have a basis, and the bases for a finite group may not have the same size. I show that bases exist for all finite abelian, dihedral, alternating, symmetric, and square-free groups.

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