Autotopies of a loop. (Russian) Zbl 0606.20060
Some questions of algebraic number theory and of constructive models, Thematic Collect. sci. Works, Alma-Ata 1985, 13-21 (1985).
[For the entire collection see Zbl 0584.00013.]
There are investigated autotopies of an arbitrary loop L. First the autotopy group of L is represented by automorphisms of the middle kernel of L. Groups of holomorphies arise by autotopies with two coinciding components. In the second part holomorphy groups are shown to be normalizers of sets of left and right translations of L in the group of all permutations of L. Finally it is proven that L is an isotopy- isomorphy loop iff the left holomorphy group of L coincides with the right holomorphy group of L.
There are investigated autotopies of an arbitrary loop L. First the autotopy group of L is represented by automorphisms of the middle kernel of L. Groups of holomorphies arise by autotopies with two coinciding components. In the second part holomorphy groups are shown to be normalizers of sets of left and right translations of L in the group of all permutations of L. Finally it is proven that L is an isotopy- isomorphy loop iff the left holomorphy group of L coincides with the right holomorphy group of L.
Reviewer: V.Havel
