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Semi-direct products and Bol loop. (English) Zbl 0831.20095
The authors first discuss under what circumstances semi-direct products of loops can be formed and then show exactly when a loop is a semi-direct product of a pair of subloops. It turns out that some ad hoc constructions in the literature are in reality semi-direct products. After this general study, the authors deal with loops satisfying the (right) Bol identity \((xy \cdot z)y = x(yz \cdot y)\), which are well known to include Bruck loops, Moufang loops, extra loops, and groups. They study the problem how to use semi-direct products of Bol loops to produce new Bol loops. Necessary and sufficient conditions are presented for a semi-direct product of loops to be a Bol loop.
Reviewer: R.Artzy (Haifa)

MSC:
20N05 Loops, quasigroups
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