an:00780935
Zbl 0831.20095
Goodaire, Edgar G.; Robinson, D. A.
Semi-direct products and Bol loop
EN
Demonstr. Math. 27, No. 3-4, 573-588 (1994).
00025503
1994
j
20N05
right Bol identity; semi-direct products of loops; Bruck loops; Moufang loops; extra loops; Bol loops
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.
R.Artzy (Haifa)