ON CLASS-PRESERVING COLEMAN AUTOMORPHISMS OF FINITE SEPARABLE GROUPS

2013 ◽  
Vol 13 (03) ◽  
pp. 1350110 ◽  
Author(s):  
JINKE HAI ◽  
ZHENGXING LI
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Separable Group ◽  
Integral Group Rings

Let G be a finite separable group. It is shown that under some conditions class-preserving Coleman automorphisms of 2-power order of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings. Our theorems generalize some well-known results.

scholarly journals Gauss Units in Integral Group Rings

1998 ◽  
Vol 204 (2) ◽  
pp. 588-596 ◽  
Author(s):  
Olaf Neisse ◽  
Sudarshan K. Sehgal
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings

scholarly journals On the Structure of Integral Group Rings of Sporadic Groups

2000 ◽  
Vol 3 ◽  
pp. 274-306 ◽  
Author(s):  
Frauke M. Bleher ◽  
Wolfgang Kimmerle
Keyword(s):  
Automorphism Groups ◽  
Symmetric Groups ◽  
Computational Procedure ◽  
Isomorphism Problem ◽  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Sporadic Groups ◽  
Integral Group Rings ◽  
Sporadic Simple Groups

AbstractThe object of this article is to examine a conjecture of Zassenhaus and certain variations of it for integral group rings of sporadic groups. We prove the ℚ-variation and the Sylow variation for all sporadic groups and their automorphism groups. The Zassenhaus conjecture is established for eighteen of the sporadic simple groups, and for all automorphism groups of sporadic simple groups G which are different from G. The proofs are given with the aid of the GAP computer algebra program by applying a computational procedure to the ordinary and modular character tables of the groups. It is also shown that the isomorphism problem of integral group rings has a positive answer for certain almost simple groups, in particular for the double covers of the symmetric groups.

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