中心循环的亚循环p-群  

Metacyclic p-group of Central Cycle

作　　者：孙秀娟 SUN Xiu-juan(School of Mathematics and Computer Science,Tangshan Teachers College,Tangshan Hebei,063000)

机构地区：[1]唐山师范学院数学与计算科学学院,河北唐山063000

出　　处：《山西大同大学学报（自然科学版）》2022年第1期25-27,共3页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：唐山师范学院科学研究基金项目[2022C38];河北省高等教育教学改革与实践项目[2019GJJG542]。

摘　　要：给出了亚循环p-群G的中心循环的条件,当p为奇素数时,中心循环的充要条件是u=r;当G是I型2-群时,中心循环充要条件是u=r;当G是Ⅱ型2-群时,中心循环充要条件是u=0且t′=r或者u=1。另外,得到了中心循环的亚循环p-群都不是p-中心p-群;对于亚循环p-群G,p为奇素数,当u<r,G是p-中心p-群。In this paper, the conditions for the central cycle of metacyclic p-groups G are given. When p is an odd prime number, the necessary and sufficient condentrition of central cycle is u=r. When G is type I of 2-groups, the necessary and sufficient condition of central cycle is u=r.When G is type Ⅱ of 2-groups, the necessary and sufficient conditions for central cycle are u=0 and t′=r or u=1. In addition, it is obtained that the metacyclic groups of central cycle are not p-central p-groups. For metacyclic p-groups with p is an odd prime number, when u<r, G is a p-central p-group.

关 键 词：循环群 亚循环群 p-中心p-群 中心 正则 

分 类 号：O152.1[理学—数学]