scholarly journals The normalizer property for integral group rings of Frobenius groups

2002 ◽  
Vol 256 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Thierry Petit Lobão ◽  
César Polcino Milies
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Frobenius Groups ◽  
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].

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.

scholarly journals Integral group rings of solvable groups with trivial central units

2018 ◽  
Vol 30 (4) ◽  
pp. 845-855 ◽  
Author(s):  
Andreas Bächle
Keyword(s):  
Solvable Group ◽  
Group Ring ◽  
Solvable Groups ◽  
Integral Group Ring ◽  
Finite Solvable Group ◽  
Group Rings ◽  
Integral Group ◽  
Frobenius Groups ◽  
Integral Group Rings ◽  
Rational Groups

Abstract The integral group ring {\mathbb{Z}G} of a group G has only trivial central units if the only central units of {\mathbb{Z}G} are {\pm z} for z in the center of G. We show that the order of a finite solvable group G with this property can only be divisible by the primes 2, 3, 5 and 7, by linking this to inverse semi-rational groups and extending one result on this class of groups. We also classify the Frobenius groups whose integral group rings have only trivial central units.

Integral group rings of frobenius groups and the conjectures of H.J. Zassenhaus

1997 ◽  
Vol 25 (7) ◽  
pp. 2311-2325 ◽  
Author(s):  
Michael A. Dokuchaev ◽  
Stanley O. Juriaans ◽  
César Polcino Milies
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Frobenius Groups ◽  
Integral Group Rings
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