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Title: A class of Bol loops with a subgroup of index two (English)
Author: Vojtěchovský, Petr
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 45
Issue: 2
Year: 2004
Pages: 371-381
Category: math
Summary: Let $G$ be a finite group and $C_2$ the cyclic group of order $2$. Consider the $8$ multiplicative operations $(x,y)\mapsto (x^iy^j)^k$, where $i$, $j$, $k\in\{-1,\,1\}$. Define a new multiplication on $G\times C_2$ by assigning one of the above $8$ multiplications to each quarter $(G\times\{i\})\times(G\times\{j\})$, for $i, j\in C_2$. We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P. Vojt\v{e}chovsk'y: On the uniqueness of loops $M(G,2)$. (English)
Keyword: Moufang loops
Keyword: loops $M(G, 2)$
Keyword: inverse property loops
Keyword: Bol loops
MSC: 20A05
MSC: 20N05
idZBL: Zbl 1101.20048
idMR: MR2075284
Date available: 2009-05-05T16:45:51Z
Last updated: 2012-04-30
Stable URL:
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