﻿ 具有小中心商的有限p-群 On the Finite p-Group with a Small Central Quotient

Pure Mathematics
Vol.07 No.04(2017), Article ID:21382,4 pages
10.12677/PM.2017.74039

On the Finite p-Group with a Small Central Quotient

Xing Wu, Yulong Ma, Hailin Liu*

School of Mathematics and Statistics, Yunnan University, Kunming Yunnan

Received: Jun. 23rd, 2017; accepted: Jul. 8th, 2017; published: Jul. 17th, 2017

ABSTRACT

Let G be a finite noncyclic p-group of order greater than. If divides, then G is called a LA-group. The purpose of this paper was to consider the class of p-group such that with the prime. We showed that such group G is LA-group.

Keywords:Finite p-Group, LA-Group, Automorphism Group

1. 引言

1)是一个PN-群和一个交换群的直积，并且整除(见 [1] )；

2)是p-交换p-群(见 [2] )；

3)，并且是亚循环的(见 [3] )；

4) (见 [4] [5] )；

5) (见 [6] )；

6)，并且是有限的模p-群(见 [7] )；

7) Frattini子群循环(见 [8] )；

8)是一个指数为的循环子群(见 [9] )；

9)是一个极大类p-群(见 [1] )；

10) 对任意的 (见 [10] )；

11) (见 [11] )；

12)是余类为2的p-群(见 [12] )。

2. 预备引理

1) 如果，那么正则；

2) 如果，那么正则；

3) 如果，并且循环，那么正则；

4) 如果，那么正则。

3. 定理证明

，则是亚交换的。

On the Finite p-Group with a Small Central Quotient[J]. 理论数学, 2017, 07(04): 297-300. http://dx.doi.org/10.12677/PM.2017.74039

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18. NOTES

*通讯作者。