Finite p-groups with a minimal non-abelian subgroup of index p (I)

被引：15
作者：
Qu, Haipeng [1 ]
Yang, Sushan [1 ]
Xu, Mingyao [1 ]
An, Lijian [1 ]
机构：
[1] Shanxi Normal Univ, Dept Math, Linfen 041004, Shanxi, Peoples R China
来源：
JOURNAL OF ALGEBRA | 2012年 / 358卷
关键词：
Minimal non-abelian p-groups; Metabelian p-groups; Regular p-groups; p-Groups of maximal class;
D O I：
10.1016/j.jalgebra.2012.03.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For an odd prime p, we classify finite p-groups with a unique minimal non-abelian subgroup of index p. In fact, such groups have a maximal quotient which is a 3-group of maximal class. This paper is a part of classification of finite p-groups with a minimal non-abelian subgroup of index p, and partly solves a problem proposed by Berkovich. (C) 2012 Elsevier Inc. All rights reserved.
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页码：178 / 188
页数：11
相关论文
共 22 条
[1]  
An L.J., FINITE P GROUP UNPUB
[2]  
Berkovich Y., 2008, GROUPS PRIME POWER O
[3]  
BERKOVICH Y, 2008, GROUPS PRIME POWER O, V2
[4]  
Berkovich Y, 2006, CONTEMP MATH, V402, P13
[5]   ON A SPECIAL CLASS OF P-GROUPS [J].
BLACKBURN, N .
ACTA MATHEMATICA, 1958, 100 (1-2) :45-92
[6]  
Blackburn N., 1961, Proc. Lond. Math. Soc., V11, P1
[7]  
Burnside W., 1897, Theory of groups of finite order
[8]  
Draganyuk S.V., 1990, COMPLEX ANAL ALGEBRA, P42
[9]  
Huppert B., 1967, Endliche Gruppen I
[10]  
Huppert B., 1953, MATH Z, V58, P243
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