生成幂零群的公平博弈
Impartial achievement games for generating nilpotent groups
AI总结：
研究Anderson和Harary提出的公平博弈，确定形如$T \ imes H$（$T$为$2$-群，$H$为奇数阶群）的有限群的nim数，涵盖所有幂零群和阿贝尔群。
摘要：
我们研究了Anderson和Harary引入的一个公平博弈。该博弈由两名玩家轮流从有限群中选择先前未被选中的元素。首先由共同选出的元素构成生成集的玩家获胜。我们确定了形如$T \ imes H$的有限群的此博弈的nim数，其中$T$是$2$-群，$H$是奇数阶群。这包括了所有幂零群，因此也包括所有阿贝尔群。
英文摘要：
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 $T \times H$, where $T$ is a $2$-group and $H$ is a group of odd order. This includes all nilpotent and hence abelian groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
