Finite Autocapable Groups with the 2-Groups of Maximal Class

被引：0

作者：

Bai, Pengfei ^{[1
]}

Guo, Xiuyun ^{[2
]}

Wang, Jiao ^{[3
]}

机构：

[1] Shanxi Univ Finance & Econ, Sch Appl Math, Taiyuan 030006, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[3] Tianjin Sino German Univ Appl Sci, Basic Courses Dept, Tianjin 300350, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2024年 / 31卷 / 04期

基金：

中国国家自然科学基金;

关键词：

autocapable group; absolute center; 2-group of maximal class; P-GROUPS; SUBGROUPS;

D O I：

10.1142/S1005386724000488

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A group H is said to be autocapable if there exists a group M such that H is isomorphic to the absolute central factor group M/L ( M ) of M. In this paper, we first prove that if N is a characteristic subgroup of an autocapable group H, then N is neither the generalized quaternion group nor the semi-dihedral group. Next, we give the classification of finite groups G if G/L ( G ) is a 2-group of maximal class.

引用

页码：651 / 660

页数：10

共 16 条

[1] AUTOMORPHISMS OF A P-GROUP [J].

ADNEY, JE ;

YEN, T .

ILLINOIS JOURNAL OF MATHEMATICS, 1965, 9 (01) :137-&

[2] Groups with abelian central quotient group [J].

Baer, Reinhold .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1938, 44 (1-3) :357-386

[3] On Finite NDC-Groups [J].

Bai, Pengfei ;

Guo, Xiuyun ;

Shum, K. P. .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (04) :3099-3123

[4]

Berkovich Y, 2008, DEGRUYTER EXPOS MATH, V46, P1, DOI 10.1515/9783110208221

[5] Finite groups with a given absolute central factor group [J].

Chaboksavar, M. ;

Ghouchan, M. Farrokhi Derakhshandeh ;

Saeedi, F. .

ARCHIV DER MATHEMATIK, 2014, 102 (05) :401-409

[6] On the Norm and Wielandt Series in Finite Groups [J].

Guo, Xiuyun ;

Zhang, Xiaohong .

ALGEBRA COLLOQUIUM, 2012, 19 (03) :411-426

[7]

Hall M., 1964, The Groups of Order, V2n

[8] THE ABSOLUTE CENTER OF A GROUP [J].

HEGARTY, P .

JOURNAL OF ALGEBRA, 1994, 169 (03) :929-935

[9] Autocommutator subgroups of finite groups [J].

Hegarty, PV .

JOURNAL OF ALGEBRA, 1997, 190 (02) :556-562

[10]

HUPPERT B., 1967, GRUND MATH WISS, V134

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