scholarly journals From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups

2014 ◽  
Vol 84 (293) ◽  
pp. 1489-1520 ◽  
Author(s):  
E. Jespers ◽  
S. O. Juriaans ◽  
A. Kiefer ◽  
A. de A. e Silva ◽  
A. C. Souza Filho
Keyword(s):  
Finite Groups ◽  
Unit Group ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Poincare Theorem

scholarly journals On the Gruenberg–Kegel graph of integral group rings of finite groups

2017 ◽  
Vol 27 (06) ◽  
pp. 619-631 ◽  
Author(s):  
W. Kimmerle ◽  
A. Konovalov
Keyword(s):  
Group Ring ◽  
Finite Groups ◽  
Prime Graph ◽  
Unit Group ◽  
Integral Group Ring ◽  
Simple Groups ◽  
Group Rings ◽  
Integral Group ◽  
Almost Simple Groups ◽  
Integral Group Rings

The prime graph question asks whether the Gruenberg–Kegel graph of an integral group ring [Formula: see text], i.e. the prime graph of the normalized unit group of [Formula: see text], coincides with that one of the group [Formula: see text]. In this note, we prove for finite groups [Formula: see text] a reduction of the prime graph question to almost simple groups. We apply this reduction to finite groups [Formula: see text] whose order is divisible by at most three primes and show that the Gruenberg–Kegel graph of such groups coincides with the prime graph of [Formula: see text].

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.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

2011 ◽  
Vol 10 (04) ◽  
pp. 711-725 ◽  
Author(s):  
J. Z. GONÇALVES ◽  
D. S. PASSMAN
Keyword(s):  
Group Ring ◽  
Unit Group ◽  
Integral Group Ring ◽  
Group Rings ◽  
Integral Group ◽  
Nonabelian Group ◽  
Ring Of Integers ◽  
Integral Group Rings ◽  
Noncyclic Subgroup

Let ℤG be the integral group ring of the finite nonabelian group G over the ring of integers ℤ, and let * be an involution of ℤG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (uk, m(x), uk, m(x*)) or (uk, m(x), uk, m(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ℤG.

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