Impartial achievement games for generating generalized dihedral groups

Bret J. Benesh, Dana C Ernst, Nandor Sieben

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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 languageEnglish (US)
Pages (from-to)371-384
Number of pages14
JournalAustralasian Journal of Combinatorics
Volume68
Issue number3
StatePublished - 2017

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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