Some Probabilistic Topics in Finite Group Theory
Date of Graduation
Summer 2006
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Les Reid
Abstract
This paper applies the theory of probability to finite groups. Three problems are addressed: the probability that any two elements in a given groups commute, the expected value of the order of an element in a given group, and the probability that a subset of a given group generates the group. For each problem, a general procedure to find the specified values for every finite group is determined. Additionally, these procedures are refined for specific types of groups, namely abelian groups, dihedral groups, generalized quaternion groups, and symmetric groups. Also, the asymptotic behavior of some of these values is explored along with some applications.
Keywords
group theory, finite groups, commutation, generation, order, probability
Subject Categories
Mathematics
Copyright
© Christie Dawn T. Bowerman
Recommended Citation
Bowerman, Christie Dawn T., "Some Probabilistic Topics in Finite Group Theory" (2006). MSU Graduate Theses. 1623.
https://bearworks.missouristate.edu/theses/1623
Dissertation/Thesis