Bret J. Benesh

collaborators

3 papers

math.GR2016

Bounds on the number of conjugacy classes of the symmetric and alternating groups

Bret Benesh, Cong Tuan Son Van

Let $G$ be a finite group with Sylow subgroups $P_{1}, \dots, P_{n}$ , and let $k (G)$ denote the number of conjugacy classes of $G$ . Pyber asked if $k (G) \leq \prod_{i = 1}^{n} k (P_{i})$ for a…

math.GR2016

Three-person impartial avoidance games for generating finite cyclic, dihedral, and nilpotent groups

Bret Benesh, Marisa Gaetz

We study a three-player variation of the impartial avoidance game introduced by Anderson and Harary. Three players take turns selecting previously-unselected elements of a finite g…

math.GR2016

Group bases for some solvable groups and semidirect products

Bret Benesh, Jason Lutz

A set $B$ is a basis for a vector space $V$ if every element of $V$ can be uniquely written as a linear combination of the elements of $B$ . There is a similar definition of a basis…