Thesis Title

Incompressible Groups

Author

Andrew Aberle

Date of Graduation

Summer 2002

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Subject Categories

Mathematics

Abstract

In group theory, Cayley's theorem states that if G is a group of order n, then G is isomorphic to a subgroup of the symmetric group, Sn. This theorem gives rise to the question: Can we improve on the index n? To consider this, we need the following definitions: A group G, with order n, is said to be incompressible if it is not isomorphic to a subgroup of Sm where m < n, and if a group G is not incompressible then it is said to be compressible. For example, we will see that Z₄ is not isomorphic to any subgroup of Sn where n<4, hence, Z₄ is incompressible. In contrast, S₃ has order 6 so by Cayley's theorem we know that S₃ is isomorphic to a subgroup of S₆. Although this is true, S₃ is clearly isomorphic to a subgroup of S₃, so it is compressible. The purpose of this paper is to prove a necessary and sufficient criterion to determine what groups of order n are incompressible.

Copyright

© Andrew Aberle

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