Math Department Colloquium
Friday, September 15 at 3:30pm to 4:30pm
Levan Center, 201 2322 N Kenmore Ave
Dana Ernst (University of Northern Arizona)
Title: Impartial achievement and avoidance games for generating finite groups
Abstract: In this talk, we will explore two impartial combinatorial games introduced by Anderson and Harary. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly selected elements wins the first game (GEN) while the first player who cannot select an element without building a generating set loses the second game (DNG). After the development of some general theory, we will discuss the strategy and corresponding nim-numbers of both games for several families of groups, including cyclic, Abelian, dihedral, generalized dihedral, symmetric, alternating, and nilpotent. This is joint work with Bret Benesh and Nandor Sieben.
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