一类中心循环的有限p-群的自同构群的研究  

A STUDY ON THE AUTOMORPHISM GROUP OF A CLASS OF A FINITE P-GROUP WITH A CYCLIC CENTER

作　　者：王玉雷[1] 刘合国[2] 吴佐慧[2] WANG Yu-lei LIU He-guo WU Zuo-hui(Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China Department of Mathematics, Hubei University, Wuhan 430062, China)

机构地区：[1]河南工业大学数学系,河南郑州450001 [2]湖北大学数学系,湖北武汉430062

出　　处：《数学杂志》2016年第6期1273-1282,共10页Journal of Mathematics

基　　金：国家自然科学基金资助(11301150;11371124);河南省自然科学基金资助(142300410134;162300410066)

摘　　要：本文研究了一类中心循环的有限p-群G的自同构群.利用在G的导群上作用平凡的自同构以及环上的辛群和正交群,确定了G的自同构群的结构,这推广了Bornand的相应结果.In this article,the automorphism group of a class of a finite p-group G with a cyclic center is researched.With the automorphisms which act trivially on the derived subgroup of G,symplectic group and orthogonal group over a ring,the structure of the automorphism group of G is determined,which generalizes the related results of Bornand.

关 键 词：有限P-群 循环中心 辛空间 自同构群 

分 类 号：O152.3[理学—数学]