scholarly journals Free normal complements and the unit group of integral group rings

1994 ◽  
Vol 122 (1) ◽  
pp. 59-59 ◽  
Author(s):  
Eric Jespers
Keyword(s):  
Unit Group ◽  
Group Rings ◽  
Integral Group ◽  
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.

scholarly journals Units and augmentation powers in integral group rings

2020 ◽  
Vol 23 (6) ◽  
pp. 931-944
Author(s):  
Sugandha Maheshwary ◽  
Inder Bir S. Passi
Keyword(s):  
Present Article ◽  
Group Ring ◽  
Unit Group ◽  
Integral Group Ring ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Natural Filtration

AbstractThe augmentation powers in an integral group ring {\mathbb{Z}G} induce a natural filtration of the unit group of {\mathbb{Z}G} analogous to the filtration of the group G given by its dimension series {\{D_{n}(G)\}_{n\geq 1}}. The purpose of the present article is to investigate this filtration, in particular, the triviality of its intersection.

scholarly journals Products of Free Groups in the Unit Group of Integral Group Rings

1996 ◽  
Vol 180 (1) ◽  
pp. 22-40 ◽  
Author(s):  
Eric Jespers ◽  
Guilherme Leal ◽  
Angel del Río
Keyword(s):  
Free Groups ◽  
Unit Group ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings

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
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