The normalizer property for integral group rings of wreath products of finite nilpotent groups by some 2-groups

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Zhengxing Li ◽  
Jinke Hai
Keyword(s):  
Nilpotent Groups ◽  
Wreath Products ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
The Normalizer Property

The normalizer property for integral group rings of holomorphs of finite nilpotent groups and the symmetric groups

2017 ◽  
Vol 16 (02) ◽  
pp. 1750025 ◽  
Author(s):  
Jinke Hai ◽  
Shengbo Ge ◽  
Weiping He
Keyword(s):  
Finite Group ◽  
Symmetric Group ◽  
Nilpotent Group ◽  
Symmetric Groups ◽  
Nilpotent Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
A Finite Group ◽  
The Normalizer Property

Let [Formula: see text] be a finite group and let [Formula: see text] be the holomorph of [Formula: see text]. If [Formula: see text] is a finite nilpotent group or a symmetric group [Formula: see text] of degree [Formula: see text], then the normalizer property holds for [Formula: see text].

Automorphisms of the integral group rings of some wreath products

1991 ◽  
Vol 19 (2) ◽  
pp. 519-534 ◽  
Author(s):  
Giambruno Antonio ◽  
Angela Valenti ◽  
Sudarshan K. Sehgal
Keyword(s):  
Wreath Products ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings

On the normalizer property for integral group rings

1999 ◽  
Vol 27 (9) ◽  
pp. 4217-4223 ◽  
Author(s):  
Yuanlin Li ◽  
S.K. Sehgal ◽  
M.M. Parmenter
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
The Normalizer Property

Finite Subgroups in Integral Group Rings

1996 ◽  
Vol 48 (6) ◽  
pp. 1170-1179 ◽  
Author(s):  
Michael A. Dokuchaev ◽  
Stanley O. Juriaans
Keyword(s):  
Solvable Groups ◽  
Nilpotent Groups ◽  
Fourth Power ◽  
Group Rings ◽  
Integral Group ◽  
Frobenius Groups ◽  
Integral Group Rings ◽  
Finite Subgroups ◽  
Generalized Quaternion

AbstractA p-subgroup version of the conjecture of Zassenhaus is proved for some finite solvable groups including solvable groups in which any Sylow p-subgroup is either abelian or generalized quaternion, solvable Frobenius groups, nilpotent-by-nilpotent groups and solvable groups whose orders are not divisible by the fourth power of any prime.

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