scholarly journals The computation of ranks of unit groups of integral group rings of finite groups

2015 ◽  
Vol 4 (1) ◽  
Keyword(s):  
Finite Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings

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.

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.

Integral Group Rings of Finite Groups

1967 ◽  
Vol 10 (5) ◽  
pp. 635-642 ◽  
Author(s):  
B. Banaschewski
Keyword(s):  
Finite Groups ◽  
Character Table ◽  
Bilinear Forms ◽  
Group Rings ◽  
Integral Group ◽  
Linear Forms ◽  
Integral Group Rings

The main object of this paper is to show that the existence of a particular kind of isomorphism between the integral group rings of two finite groups implies that the groups themselves are isomorphic. The proof employs certain types of linear forms which are first discussed in general. These linear forms are in some way related to the bilinear forms used by Weidmann [3] in showing that groups with isomorphic character rings have the same character table, and a shorter and, in a sense, more natural proof of this result is included here as another application of these linear forms.

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