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International Journal of Game Theory

, Volume 47, Issue 2, pp 451–461 | Cite as

A q-player impartial avoidance game for generating finite groups

  • Bret J. Benesh
  • Marisa R. Gaetz
Original Paper
  • 195 Downloads

Abstract

We study a q-player variation of the impartial avoidance game introduced by Anderson and Harary, where q is a prime. The game is played by the q players taking turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an element that causes the set of jointly-selected elements to be a generating set for the group, with the previous player winning. We introduce a ranking system for the other players to prevent coalitions. We describe the winning strategy for these games on cyclic, nilpotent, dihedral, and dicyclic groups.

Keywords

Group theory Game theory Impartial game Maximal subgroup 

Mathematics Subject Classification

91A46 20D30 

References

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsCollege of Saint Benedict, Saint John’s UniversitySaint JosephUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

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