On the solvable, nilpotent, and supersolvable groups of order at most two hundred

Author

Derek Keith Smith

Date of Award

8-1998

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

David Anderson

Committee Members

David Dobbs, Shashikant Mulay

Abstract

The emphasis of this paper is to determine whether a group is solvable (resp., nilpotent, supersolvable) based on its order. Throughout the thesis, a number is considered solvable (resp., nilpotent, supersolvable) if every group of that particular order is solvable (resp., nilpotent, supersolvable). Using many of the standard results for solvable groups as a blueprint, we focus primarily on finite nilpotent groups. There are three main results established in the paper. First, a finite group is nilpotent if and only if every Sylow subgroup is normal (unique). Next, a group of order p²q, for primes p < q, is nilpotent whenever p q - 1. The same principle does not hold true if p > q. And finally, the dihedral group, D_n, is nilpotent if and only if n is a power of two.

Recommended Citation

Smith, Derek Keith, "On the solvable, nilpotent, and supersolvable groups of order at most two hundred. " Master's Thesis, University of Tennessee, 1998.
https://trace.tennessee.edu/utk_gradthes/10380