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
2021 ◽  
Vol 28 (04) ◽  
pp. 561-568
Author(s):  
Jinke Hai ◽  
Lele Zhao

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.


2017 ◽  
Vol 16 (02) ◽  
pp. 1750025 ◽  
Author(s):  
Jinke Hai ◽  
Shengbo Ge ◽  
Weiping He

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].


2013 ◽  
Vol 12 (06) ◽  
pp. 1350004 ◽  
Author(s):  
JAIRO Z. GONÇALVES ◽  
ÁNGEL DEL RÍO

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.


1999 ◽  
Vol 27 (9) ◽  
pp. 4217-4223 ◽  
Author(s):  
Yuanlin Li ◽  
S.K. Sehgal ◽  
M.M. Parmenter

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