THE NORMALIZER PROPERTY FOR INTEGRAL GROUP RINGS OF WREATH PRODUCTS OF FINITE NILPOTENT GROUPS BY CYCLIC GROUPS

被引：9

作者：

Li, Zhengxing ^{[1
,2
]}

Hai, Jinke ^{[2
]}

机构：

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

[2] Qingdao Univ, Sch Math, Qingdao 266071, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2011年 / 39卷 / 02期

关键词：

Extensive subgroups; Normalizer property; Semidirect products; Wreath products; AUTOMORPHISMS;

D O I：

10.1080/00927871003591975

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G = NwrC(n) be the wreath product of N by C(n), where N is a finite nilpotent group and C(n) is a cyclic group of order n. Then the normalizer property holds for G.

引用

页码：521 / 533

页数：13

共 50 条

[31] GROTHENDIECK GROUPS OF INTEGRAL NILPOTENT GROUP-RINGS
MIYAMOTO, M
[J]. JOURNAL OF ALGEBRA, 1984, 91 (01) : 32 - 35
[32] The influence of maximal quotient groups on the normalizer conjecture of integral group rings
Li, Zhengxing
Li, Yuanlin
Gao, Hongwei
[J]. JOURNAL OF GROUP THEORY, 2016, 19 (06) : 983 - 992
[33] Finite matrix groups over nilpotent group rings
Marciniak, ZS
Sehgal, SK
[J]. JOURNAL OF ALGEBRA, 1996, 181 (02) : 565 - 583
[34] Wreath products of finite groups by quantum groups
Freslon, Amaury
Skalski, Adam
[J]. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2018, 12 (01) : 29 - 68
[35] INTEGRAL GROUP-RINGS WITH RESIDUALLY NILPOTENT UNIT GROUPS
MUSSON, I
WEISS, A
[J]. ARCHIV DER MATHEMATIK, 1982, 38 (06) : 514 - 530
[36] Fusion Procedure for Wreath Products of Finite Groups by the Symmetric Group
L. Poulain d’Andecy
[J]. Algebras and Representation Theory, 2014, 17 : 809 - 830
[37] Fusion Procedure for Wreath Products of Finite Groups by the Symmetric Group
d'Andecy, L. Poulain
[J]. ALGEBRAS AND REPRESENTATION THEORY, 2014, 17 (03) : 809 - 830
[38] Characters of wreath products of finite groups with the infinite symmetric group
Hirai, T
Hirai, E
[J]. JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2005, 45 (03): : 547 - 597
[39] Varieties Generated by Wreath Products of Abelian and Nilpotent Groups
Mikaelian, V. H.
[J]. ALGEBRA AND LOGIC, 2015, 54 (01) : 70 - 73
[40] Varieties Generated by Wreath Products of Abelian and Nilpotent Groups
V. H. Mikaelian
[J]. Algebra and Logic, 2015, 54 : 70 - 73

← 1 2 3 4 5 →