5 citations · 8 across the 11 of their papers we have counts for
5 papers · 1 filter
Impartial achievement games for generating generalized dihedral groups
Bret J. Benesh, Dana C. Ernst, Nandor Sieben
We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unselected elements of a finite group. The first…
Bounds on the number of conjugacy classes of the symmetric and alternating groups
Bret Benesh, Cong Tuan Son Van
Let be a finite group with Sylow subgroups , and let denote the number of conjugacy classes of . Pyber asked if for a…
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…
Group bases for some solvable groups and semidirect products
Bret Benesh, Jason Lutz
A set is a basis for a vector space if every element of can be uniquely written as a linear combination of the elements of . There is a similar definition of a basis…
On two questions by Finch and Jones about perfect order subset groups
Bret J. Benesh
A finite group G is said to be a POS-group if the number of elements of every order occurring in G divides |G|. We answer two questions by Finch and Jones by providing an infinite…