Griess, Robert L. jun. Codes, loops and \(p\)-locals. (English) Zbl 0865.94030 Arasu, K. T. (ed.) et al., Groups, difference sets, and the Monster. Proceedings of a special research quarter, Columbus, OH, USA, Spring 1993. Berlin: Walter de Gruyter. Ohio State Univ. Math. Res. Inst. Publ. 4, 369-375 (1996). This paper is a review of the developments of the theory of “code loops”. These special Moufang loops were introduced by R. Parker and used by J. H. Conway [Invent. Math. 79, 513-540 (1985; Zbl 0564.20010)] to provide a new construction of the Fischer-Griess Monster [R. L. Griess, Invent. Math. 69, 1-102 (1982; Zbl 0498.20013)]. In this paper the author summarizes the results of the concept of loops which is effectively used in the theory of simple groups, Lie groups, nonassociative algebras, in algebraic coding theory etc.For the entire collection see [Zbl 0836.00028]. Reviewer: P.Lakatos (Debrecen) MSC: 94B25 Combinatorial codes 20D08 Simple groups: sporadic groups 20N05 Loops, quasigroups Keywords:loop; \(p\)-locals; sporadic groups; Moufang loops; Fischer-Griess Monster Citations:Zbl 0564.20010; Zbl 0498.20013 × Cite Format Result Cite Review PDF