The Normalizer Property for Integral Group Rings of Holomorphs of Finite Groups with Trivial Center

2020 ◽  
Vol 36 (4) ◽  
pp. 401-406
Author(s):  
Jin Ke Hai ◽  
Yi Xin Zhu
Keyword(s):  
Finite Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Trivial Center ◽  
The Normalizer Property

Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups

2021 ◽  
Vol 28 (04) ◽  
pp. 561-568
Author(s):  
Jinke Hai ◽  
Lele Zhao
Keyword(s):  
Abelian Group ◽  
Simple Group ◽  
Finite Groups ◽  
Finite Simple Group ◽  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Inner Automorphism ◽  
Coleman Automorphism

Let [Formula: see text] be an extension of a finite characteristically simple group by an abelian group or a finite simple group. It is shown that every Coleman automorphism of [Formula: see text] is an inner automorphism. Interest in such automorphisms arises from the study of the normalizer problem for integral group rings.

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].

A SURVEY ON FREE SUBGROUPS IN THE GROUP OF UNITS OF GROUP RINGS

2013 ◽  
Vol 12 (06) ◽  
pp. 1350004 ◽  
Author(s):  
JAIRO Z. GONÇALVES ◽  
ÁNGEL DEL RÍO
Keyword(s):  
Finite Groups ◽  
Free Groups ◽  
Group Algebras ◽  
Group Rings ◽  
Integral Group ◽  
Natural Group ◽  
Integral Group Rings ◽  
Group Of Units ◽  
Survey Results ◽  
Free Subgroups

In this survey we revise the methods and results on the existence and construction of free groups of units in group rings, with special emphasis in integral group rings over finite groups and group algebras. We also survey results on constructions of free groups generated by elements which are either symmetric or unitary with respect to some involution and other results on which integral group rings have large subgroups which can be constructed with free subgroups and natural group operations.

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
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