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- W4300830872 abstract "A left Bol loop is a loop satisfying $x(y(xz)) = (x(yx))z$. The commutant of a loop is the set of elements which commute with all elements of the loop. In a finite Bol loop of odd order or of order $2k$, $k$ odd, the commutant is a subloop. We investigate conditions under which the commutant of a Bol loop is not a subloop. In a finite Bol loop of order relatively prime to 3, the commutant generates an abelian group of order dividing the order of the loop. This generalizes a well-known result for Moufang loops. After describing all extensions of a loop $K$ such that $K$ is in the left and middle nuclei of the resulting loop, we show how to construct classes of Bol loops with non-subloop commutant. In particular, we obtain all Bol loops of order 16 with non-subloop commutant." @default.
- W4300830872 created "2022-10-04" @default.
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- W4300830872 date "2006-01-14" @default.
- W4300830872 modified "2023-09-27" @default.
- W4300830872 title "When is the commutant of a Bol loop a subloop?" @default.
- W4300830872 doi "https://doi.org/10.48550/arxiv.math/0601363" @default.
- W4300830872 hasPublicationYear "2006" @default.
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