Matrices over centrally -graded rings.
On the Isomorphism of Group Algebras.
Nilpotent Elements in Group Rings.
Isomorphism of Modular Group Algebras.
On a Conjecture of Zassenhaus on Torsion Units in Integral Group Rings.
Group Rings Whose Units Form an FC-Group.
Group Rings Whose Units Form an FC-Group.
Certain normal subgroups of units in group rings.
Unitary subgroup of integral group rings.
Let A be a finite abelian group and G = A x 〈b〉, b = 1, a = a, ∀a ∈ A. We find generators up to finite index of the unitary subgroup of ZG. In fact, the generators are the bicyclic units. For an arbitrary group G, let B(ZG) denote the group generated by the bicyclic units. We classify groups G such that B(ZG) is unitary.
Torsion matrices over commutative integral group rings.
Let ZA be the integral group ring of a finite abelian group A, and n a positive integer greater than 5. We provide conditions on n and A under which every torsion matrix U, with identity augmentation, in GL(ZA) is conjugate in GL(QA) to a diagonal matrix with group elements on the diagonal. When A is infinite, we show that under similar conditions, U has a group trace and is stably conjugate to such a diagonal matrix.
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