Achievement and avoidance games for generating abelian groups |
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Authors: | M Anderson F Harary |
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Institution: | 1. Department of Mathematics, Colorado College, 80903, Colorado Springs, CO 2. Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI 3. New Mexico State University, 88003, Lass Cruces, NM
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Abstract: | For any finite groupG, the DO GENERATE game is played by two players Alpha and Beta as follows. Alpha moves first and choosesx 1 ∈G. Thek-th play consists of a choice ofx k ∈G ?S k ?1 whereS n ={itx 1,...,x n }. LetG n = 〈S n 〉. The game ends whenG n =G. The player who movesx n wins. In the corresponding avoidance game, DON'T GENERATE, the last player to move loses. Of course neither game can end in a draw. For an arbitrary group, it is an unsolved problem to determine whether Alpha or Beta wins either game. However these two questions are answered here for abelian groups. |
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