Some Probabilistic Topics in Finite Group Theory
Christie Dawn T. Bowerman · BearWorks (Missouri State University) · 2006
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.