On nilpotent Moufang loops with central associators

被引：12
作者：
Nagy, Gabor P.
Valsecchi, Mattrizio
机构：
[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary
[2] Univ Erlangen Nurnberg, Math Inst, D-91054 Erlangen, Germany
来源：
JOURNAL OF ALGEBRA | 2007年 / 307卷 / 02期
基金：
匈牙利科学研究基金会;
关键词：
Moufang loops; nilpotent loops; loops of maximal class; semidirect product of loops;
D O I：
10.1016/j.jalgebra.2006.01.031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we investigate Moufang p-loops of nilpotency class at least three for p > 3. The smallest examples have order p(5) and satisfy the following properties: (1) They are of maximal nilpotency class, (2) their associators lie in the center, and (3) they can be constructed using a general form of the semidirect product of a cyclic group and a group of maximal class. We present some results concerning loops with these properties. As an application, we classify proper Moufang loops of order p(5), p > 3, and collect information on their multiplication groups. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：547 / 564
页数：18
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