The Spectrum of Nim-Values for Achievement Games for Generating Finite Groups
Bret J. Benesh, Dana C. Ernst, Nándor Sieben · arXiv (Cornell University) · 2020
We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The game ends when the jointly selected elements generate the group. The last player able to make a move is the winner of the game. We prove that the spectrum of nim-values of these games is $\{0,1,2,3,4\}$. This positively answers two conjectures from a previous paper by the last two authors.