Outer automorphism groups of finite p-nilpotent groups

被引：0

作者：

Jin, P ^{[1
]}

机构：

[1] Shanxi Univ, Dept Math, Taiyuan 030006, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2002年 / 30卷 / 09期

关键词：

D O I：

10.1081/AGB-120013324

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

When does a finite group possess a non-trivial outer automorphism? In this paper for a finite p-nilpotent group G we shall prove the following results. (a) If \O-p(G)\ > p, then p divides the order of Out(G). (b) If O-p(G) is non-abelian, then p divides the order of C-Out(G) (Z(G)). Our results extend a famous theorem of Gaschutz and can be applied to the investigation of finite complete groups.

引用

页码：4369 / 4375

页数：7

共 50 条

[1] On finite p-nilpotent groups
Adolfo Ballester-Bolinches
Xiuyun Guo
Yangming Li
Ning Su
Monatshefte für Mathematik, 2016, 181 : 63 - 70
[2] On finite p-nilpotent groups
Ballester-Bolinches, Adolfo
Guo, Xiuyun
Li, Yangming
Su, Ning
MONATSHEFTE FUR MATHEMATIK, 2016, 181 (01): : 63 - 70
[3] A Criterion on the Finite p-Nilpotent Groups
Xiangyang XU
Yangming LI
JournalofMathematicalResearchwithApplications, 2019, 39 (03) : 254 - 258
[4] Characterization of p-Nilpotent Groups by Monomials of Finite Groups
Iiyori, Nobuo
COMMUNICATIONS IN ALGEBRA, 2010, 38 (05) : 1695 - 1698
[5] A characteristic property of finite p-nilpotent groups
Al-Sharo, KA
COMMUNICATIONS IN ALGEBRA, 2004, 32 (07) : 2655 - 2657
[6] p-Nilpotent Maximal Subgroups in Finite Groups
Beltran, Antonio
Shao, Changguo
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2025, 22 (01)
[7] COHOMOLOGICAL TRIVIALITY AND FINITE P-NILPOTENT GROUPS
BABAKHANIAN, A
ARCHIV DER MATHEMATIK, 1970, 21 (01) : 40 - +
[8] On p-nilpotent groups and metabelian groups
Zhang, Linhua
Fu, Shilu
Chongqing Jianzhu Daxue Xuebao/Journal of Chongqing Jianzhu University, 2000, 22 (01): : 93 - 96
[9] ANOTHER HOMOLOGICAL CHARACTERIZATION OF FINITE P-NILPOTENT GROUPS
STAMMBACH, U
MATHEMATISCHE ZEITSCHRIFT, 1977, 156 (02) : 209 - 210
[10] FINITE GROUPS WITH p-NILPOTENT OR Φ-SIMPLE MAXIMAL SUBGROUPS
Bazhanova, E. N.
Vedernikov, V. A.
SIBERIAN MATHEMATICAL JOURNAL, 2022, 63 (01) : 19 - 33

← 1 2 3 4 5 →