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.

引用

页数：12

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