Impartial achievement games for generating nilpotent groups-Reference-Cited by-同舟云学术

Impartial achievement games for generating nilpotent groups

Published:2018-12-18 Issue:3 Volume:22 Page:515-527
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Benesh Bret J.¹,Ernst Dana C.²,Sieben Nándor²

Affiliation:

1. Department of Mathematics , College of Saint Benedict and Saint John’s University , 37 College Avenue South , Saint Joseph , MN 56374-5011 , USA

2. Department of Mathematics and Statistics , Northern Arizona University , PO Box 5717 , Flagstaff , AZ 86011-5717 , USA

Abstract

Abstract We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for finite groups of the form T × H

{T\times H}

, where T is a 2-group and H is a group of odd order. This includes all nilpotent and hence abelian groups.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference13 articles.

1. M. H. Albert, R. J. Nowakowski and D. Wolfe, Lessons in Play: An Introduction to Combinatorial Game Theory, CRC Press, Boca Raton, 2007.

2. M. Anderson and F. Harary, Achievement and avoidance games for generating abelian groups, Internat. J. Game Theory 16 (1987), no. 4, 321–325.

3. F. W. Barnes, Some games of F. Harary, based on finite groups, Ars Combin. 25A (1988), 21–30.

4. B. J. Benesh, D. C. Ernst and N. Sieben, Impartial avoidance and achievement games for generating symmetric and alternating groups, Int. Electron. J. Algebra 20 (2016), 70–85.

5. B. J. Benesh, D. C. Ernst and N. Sieben, Impartial avoidance games for generating finite groups, North-Western European J. Math. 2 (2016), 83–102.

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