Split extension in Moufang loops

被引:0
|
作者
Leong, F [1 ]
Rajah, A [1 ]
机构
[1] Univ Sains Malaysia, Sch Math Sci, Pulau Pinang 11800, Malaysia
来源
PUBLICATIONES MATHEMATICAE-DEBRECEN | 1998年 / 52卷 / 1-2期
关键词
Moufang loop; normal; extension; simple loop;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we prove the following: 1. Let G be a Moufang loop of order p(alpha)m, (p, m) = 1, (p-1, p(alpha)m,) = 1 and p is a prime. Suppose G has an element of order p(alpha). Then G = P x K, a split extension of a normal subloop K of order m with a subloop P order p(alpha). 2. Let G be a Moufang loop of odd order p(2)m, (p, m) = 1, and p is the smallest prime dividing \G\. Then a similar result holds as in (1) with alpha = 2.
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页码:33 / 42
页数:10
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