Loops related to geometric structures. (English) Zbl 1134.20068
The author discusses in this paper relations like the use of geometric structures (chain structures, graphs) to represent loops. With derivations like loop derivation, permutation derivation of a loop \((P,+)\) the author translates properties of one structure into properties of the other. Of particular interest to the author are invariant reflection structures \((P,\;)\) and their corresponding K-loops. The author discusses also: symmetric chain structures, immersions of permutation sets in chain structures, loops derived from point reflection spaces, loops with fibrations.
Reviewer: C. Pereira da Silva (Curitiba)
MSC:
20N05 | Loops, quasigroups |
51F05 | Absolute planes in metric geometry |
51A25 | Algebraization in linear incidence geometry |