幂结合共轭闭环
Power-associative, conjugacy closed loops
摘要：
研究了共轭闭回路（CC-回路）和幂结合CC-回路（PAC-回路）。如果$Q$是一个以$N$为核的PAC-环，那么$Q/N$是一个指数为12的阿贝尔群;如果另外$Q$是有限的，那么$|Q|$可以被16或27整除。有八个16阶的非关联PAC循环，其中三个不是额外的循环。有八个27阶的非结合PAC-循环，其中四个具有自守逆属性。我们还研究了循环中的一些特殊元素，如Moufang元素、弱逆性元素和额外元素。在CC-循环中，循环的集合和额外元素的集合是正常的子循环。对于PACC循环中的每个$c$，$c^3$是额外的，$c^6$是额外的，而$c^{12} \in N$。
英文摘要：
We study conjugacy closed loops (CC-loops) and power-associative CC-loops (PACC-loops). If $Q$ is a PACC-loop with nucleus $N$, then $Q/N$ is an abelian group of exponent 12; if in addition $Q$ is finite, then $|Q|$ is divisible by 16 or by 27. There are eight nonassociative PACC-loops of order 16, three of which are not extra loops. There are eight nonassociative PACC-loops of order 27, four of which have the automorphic inverse property. We also study some special elements in loops, such as Moufang elements, weak inverse property (WIP) elements, and extra elements. In a CC-loop, the set of WIP and the set of extra elements are normal subloops. For each $c$ in a PACC-loop, $c^3$ is WIP, $c^6$ is extra, and $c^{12} \in N$.
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