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A note on simple groups and simple loops. (English) Zbl 0954.20039
Baik, Young Gheel (ed.) et al., Groups - Korea ’98. Proceedings of the 4th international conference, Pusan, Korea, August 10-16, 1998. Berlin: Walter de Gruyter. 305-317 (2000).
From the author’s abstract: “We detail a research program that attempts to realize finite simple groups as (right) multiplication groups of simple (right) loops. This realization is part of an even larger program whose ultimate goal is to understand the mysterious relationship between nonassociativity, as embodied in (right) loops, and associativity, as embodied in groups. This paper is intended as an introduction to this larger program.” The sections of the paper: 1. Groupoids and quasigroups, 2. Multiplication semigroups, 3. Right transversals and right loops, 4. Right multiplication groups as quotients, 5. Multiplication groups, 6. Simple groups, 7. Moufang loops, 8. Glauberman’s $$\rho$$ extended: groups with triality, 9. Simple groups with triality.
For the entire collection see [Zbl 0933.00033].
Reviewer: R.Artzy (Haifa)

##### MSC:
 20N05 Loops, quasigroups 20D05 Finite simple groups and their classification