论文标题
汽车循环和Metabelian组
Automorphic loops and metabelian groups
论文作者
论文摘要
给定一个独特的2分组$ g $，我们研究了\ cite {baer}的施工而产生的交换环$（g，\ circ）$。我们调查了$ \ circ $的一些一般属性和应用程序，并确定$ g $的必要条件，以便为$（g，\ circ）$作为moufang。在\ cite {greer14}中，猜测$ g $是metabelian，并且仅当$（g，\ circ）$是自动循环时。我们以肯定的方式回答了这一猜想的一部分：特别是，我们表明，如果$ g $是一个拆分的metabelian奇数订单组，则$（g，\ circ）$是自动形态。
Given a uniquely 2-divisible group $G$, we study a commutative loop $(G,\circ)$ which arises as a result of a construction in \cite{baer}. We investigate some general properties and applications of $\circ$ and determine a necessary and sufficient condition on $G$ in order for $(G, \circ)$ to be Moufang. In \cite{greer14}, it is conjectured that $G$ is metabelian if and only if $(G, \circ)$ is an automorphic loop. We answer a portion of this conjecture in the affirmative: in particular, we show that if $G$ is a split metabelian group of odd order, then $(G, \circ)$ is automorphic.
