A characterization of nilpotent Moufang loops of odd order

被引：1
|
作者：
Csorgo, Piroska [1 ]
机构：
[1] Eszterhazy Karoly Coll, Inst Math, Leanyka U 4, H-3300 Eger, Hungary
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2016年 / 15卷 / 10期
关键词：
Moufang loop; nucleus; center; commutant; multiplication group; inner mapping group; central nilpotence;
D O I：
10.1142/S0219498816501838
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Glauberman and Wright in [G. G. Glauberman and C. R. B. Wright, Nilpotence of finite Moufang 2-loops, J. Algebra 8 (1968) 415-417] proved that a nilpotent Moufang loop is the direct product of p-loops for some primes p, consequently the elements of coprime order commute in a nilpotent Moufang loop. In this paper, we prove that in Moufang loops of odd order this condition is equivalent to the central nilpotence.
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页数：12
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