换位子群为p阶群的有限p-群的自同构群(Ⅱ)  

The automorphism group of a finite p-group with derived subgroup of prime order(Ⅱ)

作　　者：徐行忠[1] 刘合国[2] 

机构地区：[1]北京大学数学科学学院,北京100871 [2]湖北大学数学系,武汉430062

出　　处：《中国科学：数学》2012年第1期1-11,共11页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10971054)资助项目

摘　　要：本文给出了换位子群为p阶群的有限p-群的自同构群的结构定理的两点应用:其一,直接导出某些有限p-群的自同构群的结构;其二,对换位子群为p阶群的有限p-群,确定了其自同构群的阶何时达到最大值和最小值.In this paper, we give two applications of the theorem about the automorphism group of a finite p-group with derived subgroup of prime order. First, we use the theorem to prove some well-known results about automorphisms of some finite p-groups directly. Second, let G be a finite p-group with derived subgroup of prime order, we give the conditions when the order of AutG attains the maximal value or minimal value, respectively.

关 键 词：有限P-群 自同构群 换位子群 

分 类 号：O152.1[理学—数学]