The Spectrum of Nim-Values for Achievement Games for Generating Finite Groups

Authors

Bret J. Benesh, College of Saint Benedict/Saint John's UniversityFollow
Dana C. Ernst
Nándor Sieben

Document Type

Article

Publication Date

7-21-2023

Disciplines

Mathematics | Number Theory

Abstract

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.

Copyright Statement

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

Benesh BJ, Ernst DC, Sieben N. 2023. The spectrum of nim-values for achievement games for generating finite groups. Integers 23. https://doi.org/10.5281/zenodo.8174526