The isomorphic description of torsion units in commutative group rings over fields with positive characteristic.
The special circulant matrix and units in group rings.
The structure of the unit group of the group algebra
The structure of the unit group of the group algebra of the group over any finite field of characteristic 2 is established in terms of split extensions of cyclic groups.
The unit group of .
The unit groups of semisimple group algebras of some non-metabelian groups of order
We consider all the non-metabelian groups of order that have exponent either or and deduce the unit group of semisimple group algebra . Here, denotes the power of a prime, i.e., for prime and a positive integer . Up to isomorphism, there are groups of order that have exponent either or . Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order that are a direct product of two nontrivial...
Torsion units for some almost simple groups
We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on partial augmentations for torsion units of integral group rings have improved the effectiveness of the Luther-Passi method for verifying the Zassenhaus conjecture for certain groups. We prove that the Zassenhaus conjecture is true for the automorphism group of the simple group . Additionally we prove that...
Torsion units in group rings.
Let U(RG) be the unit group of the group ring RG. In this paper we study group rings RG whose support elements of every torsion unit are torsion, where R is either the ring of integers Z or a field K.
Torsion units in integral group rings.
Trivial units in commutative group algebras.