Impartial achievement games for generating generalized dihedral groups

Bret J. Benesh; Dana C Ernst; Nandor Sieben

Impartial achievement games for generating generalized dihedral groups

Bret J. Benesh, Dana C Ernst, Nandor Sieben

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unsel-ected 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 generalized dihedral groups, which are of the form Dih(A) = Z₂ ⋉ A for a finite abelian group A.

Original language	English (US)
Pages (from-to)	371-384
Number of pages	14
Journal	Australasian Journal of Combinatorics
Volume	68
Issue number	3
State	Published - 2017

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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title = "Impartial achievement games for generating generalized dihedral groups",

abstract = "We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unsel-ected 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 generalized dihedral groups, which are of the form Dih(A) = Z2 ⋉ A for a finite abelian group A.",

author = "Benesh, {Bret J.} and Ernst, {Dana C} and Nandor Sieben",

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AU - Ernst, Dana C

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AB - We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unsel-ected 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 generalized dihedral groups, which are of the form Dih(A) = Z2 ⋉ A for a finite abelian group A.

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Impartial achievement games for generating generalized dihedral groups

Abstract

ASJC Scopus subject areas

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