阿贝尔群与极大类p-群的半直积的Coleman自同构

数学物理学报 ›› 2012, Vol. 32 ›› Issue (2): 344-348.

阿贝尔群与极大类p-群的半直积的Coleman自同构

李正兴, 海进科

青岛大学数学科学学院山东青岛 266071

收稿日期:2010-07-08 修回日期:2011-12-06 出版日期:2012-04-25 发布日期:2012-04-25
基金资助:
国家自然科学基金(11071155, 11171169)和山东省自然科学基金(Y2008A03)资助

Coleman Automorphisms of Semidirect Products of Abelian Groups by p-groups of Maximal Class

LI Zheng-Xing, HAI Jin-Ke

College of Mathematics, Qingdao University, Shandong Qingdao 266071

Received:2010-07-08 Revised:2011-12-06 Online:2012-04-25 Published:2012-04-25
Supported by:
国家自然科学基金(11071155, 11171169)和山东省自然科学基金(Y2008A03)资助

摘要/Abstract

摘要：

设G=A\×P是阿贝尔群$A$与极大类p -群P的半直积, 其中P中的元以幂自同构的方式作用于A. 该文证明了G的每个Coleman自同构都是内自同构.作为该结果的一个直接推论, 作者得到了这样的群$G$有正规化子性质.

关键词: 整群环, Coleman自同构, 正规化子性质

Abstract:

Let G=A×P be the semidirect product of an abelian group A and a p-group P of maximal class, where P acts on A by leaving every cyclic subgroup of A invariant. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence, we obtain that the normalizer property holds for such group G.

Key words: Integral group ring, Coleman automorphism, Normalizer property

中图分类号:

20C05

李正兴, 海进科. 阿贝尔群与极大类p-群的半直积的Coleman自同构[J]. 数学物理学报, 2012, 32(2): 344-348.

LI Zheng-Xing, HAI Jin-Ke. Coleman Automorphisms of Semidirect Products of Abelian Groups by p-groups of Maximal Class[J]. Acta mathematica scientia,Series A, 2012, 32(2): 344-348.

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