Commentationes mathematicae Universitatis Carolinae | |
Quasigroups arisen by right nuclear extension | |
Péter T. Nagy1  | |
关键词: extension of quasigroups; right nucleus; quasigroup with right unit; transversal; | |
DOI : | |
学科分类:物理化学和理论化学 | |
来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics | |
【 摘 要 】
The aim of this paper is to prove that a quasigroup $Q$ with right unit is isomorphic to an $f$-extension of a right nuclear normal subgroup $G$ by the factor quasigroup $Q/G$ if and only if there exists a normalized left transversal $\Sigma \subset Q$ to $G$ in $Q$ such that the right translations by elements of $\Sigma $ commute with all right translations by elements of the subgroup $G$. Moreover, a loop $Q$ is isomorphic to an $f$-extension of a right nuclear normal subgroup $G$ by a loop if and only if $G$ is middle-nuclear, and there exists a normalized left transversal to $G$ in $Q$ contained in the commutant of~$G$.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO201901230834320ZK.pdf | 73KB | download |