极大子群为广义四元数群的有限2-群  

Finite 2-Groups with a Maximal Subgroup Isomorphic to a Generalized Quaternion Group

作　　者：郝成功[1] 王建婷 

机构地区：[1]山西大学数学科学学院,太原030006

出　　处：《山西大学学报（自然科学版）》2017年第4期732-735,共4页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省自然科学基金(2012011001-1)

摘　　要：从对合的角度研究了具有一个极大子群为广义四元数群的有限2-群的结构,通过考察广义四元数群的对合自同构的共轭类,以及相应半直积中的对合个数,获得了上述2-群的结构的完整分类。作为推论,证明了对合个数是该类2-群的同构型的一个完全不变量。From the aspect of involutions, finite 2-groups with a maximal subgroup isomorphic to a generalized quaternion group are studied. By investigating the conjugacy classes of involution automorphisms and the number of involutions in the corresponding semi-direct products, a complete classification of such 2- groups is obtained. As a corollary, the number of involutions in such a 2-group is shown to be a completely invariant under isomorphisms.

关 键 词：2-群 极大子群 对合 广义四元数群 自同构群 

分 类 号：O152.1[理学—数学]