Free groups in subnormal subgroups and the residual nilpotence of the group of units of groups rings
JZ Gonçalves - Canadian Mathematical Bulletin, 1984 - cambridge.org
Let KG be the group ring of the group G over the field K and U (KG) its unit group. When G is
finite we derive conditions which imply that every noncentral subnormal subgroup of U (KG) …
finite we derive conditions which imply that every noncentral subnormal subgroup of U (KG) …
Group algebras with units satisfying a group identity
CH Liu - Proceedings of the American Mathematical Society, 1999 - ams.org
Let $ K [G] $ be the group algebra of a group $ G $ over a field $ K $, and let $ U (K [G]) $ be
its group of units. A conjecture by Brian Hartley asserts that if $ G $ is a torsion group and …
its group of units. A conjecture by Brian Hartley asserts that if $ G $ is a torsion group and …
Group algebras whose units satisfy a group identity
GROUP ALGEBRAS WHOSE UNITS SATISFY A GROUP IDENTITY 1. Introduction The unit
group U = U(FG) is said to satisfy a group identity Page 1 PROCEEDINGS OF THE AMERICAN …
group U = U(FG) is said to satisfy a group identity Page 1 PROCEEDINGS OF THE AMERICAN …
Free subgroups in almost subnormal subgroups of general skew linear groups
N Ngoc, M Bien, B Hai - St. Petersburg Mathematical Journal, 2017 - ams.org
Let $ D $ be a weakly locally finite division ring and $ n $ a positive integer. The problem
under study concerns the existence of noncyclic free subgroups in noncentral almost …
under study concerns the existence of noncyclic free subgroups in noncentral almost …
Symmetric units and group identities
In this paper we study rings R with an involution whose symmetric units satisfy a group
identity. An important example is given by FG, the group algebra of a group G over a field F; …
identity. An important example is given by FG, the group algebra of a group G over a field F; …
Group identities on units of group algebras
Let U be the group of units of the group algebra FG of a group G over a field F. Suppose that
either F is infinite or G has an element of infinite order. We characterize groups G so that U …
either F is infinite or G has an element of infinite order. We characterize groups G so that U …
Graded identities of matrix algebras and the universal graded algebra
E Aljadeff, D Haile, M Natapov - Transactions of the American Mathematical …, 2010 - ams.org
We consider fine group gradings on the algebra $ M_n (\mathbb {C}) $ of $ n $ by $ n $
matrices over the complex numbers and the corresponding graded polynomial identities …
matrices over the complex numbers and the corresponding graded polynomial identities …
A note on the existence of non-cyclic free subgroups in division rings
BX Hai, NK Ngoc - Archiv der Mathematik, 2013 - Springer
A division ring D is said to be weakly locally finite if for every finite subset S ⊂ DS⊂ D, the
division subring of D generated by S is centrally finite. It is known that the class of weakly …
division subring of D generated by S is centrally finite. It is known that the class of weakly …
Integral group rings: Groups of units and classical K-theory
VA Artamonov, AA Bovdi - Journal of Soviet Mathematics, 1991 - Springer
This survey contains results obtained in this area from the second half of the sixties to the
present time. In the group of units of the group ring, normal periodic subgroups, elements of …
present time. In the group of units of the group ring, normal periodic subgroups, elements of …
Group identities on symmetric units
Let F be an infinite field of characteristic different from 2, G a group and∗ an involution of G
extended by linearity to an involution of the group algebra FG. Here we completely …
extended by linearity to an involution of the group algebra FG. Here we completely …