Uniqueness theorems for global mixed groups.
Uniserial groups.
Unit groups of group algebras of some small groups
Let be a group algebra of a group over a field and the unit group of . It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group with order over any finite field of characteristic is established. We also characterize the structure of the unit group of over any finite field of characteristic and the structure of...
Unital Rings whose Additive Endomorphisms Commute.
Unitary Groups Over Compact Valuation Rings.
Unitary Reflection Groups and Cohomology.
Unitary subgroup of integral group rings.
Let A be a finite abelian group and G = A x 〈b〉, b2 = 1, ab = a-1, ∀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 B2(ZG) denote the group generated by the bicyclic units. We classify groups G such that B2(ZG) is unitary.
Unitary subgroup of integral groups rings.
Unitary units in modular group algebras.
Units in group rings of crystallographic groups
In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the infinite dihedral...
Units in quasigroups with classical Bol--Moufang type identities
We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups with classical Bol--Moufang type identities, listed in paper Extra loops II, by F. Fenyves (1969). We consider those Bol--Moufang identities where it has not been decided yet whether a quasigroup fulfilling this identity has to possess a left or right identity. We also provide a table of all Moufang--Bol identities, indicating at each whether it describes the variety of groups, and whether it forces...
Units of F5kD10
2000 Mathematics Subject Classification: 20C05, 16U60, 16S84, 15A33.The Structure of the Unit Group of the Group Algebra of the group D10 over any field of characteristic 5 is established in terms of split extensions of cyclic groups.
Units of the string link monoids
We show that the map obtained by viewing a geometric (i.e. representative) braid as a string link induces an isomorphism of the n-strand braid group onto the group of units of the n-strand string link monoid.
Universal coextensions within a variety.
Universal cyclic relations
Universal expansion of semigroup varieties by regular involution.
Universal groups on semilattices of reversible cancellative semigroups .
Universal semigroups.
Universal transitivity of simple and 2-simple prehomogeneous vector spaces
We denote by a field of characteristic zero satisfying . Let be a connected -split linear algebraic group acting on rationally by with a Zariski-dense -orbit . A prehomogeneous vector space ,X) is called “universally transitive” if the set of -rational points is a single
Universality property of free groupoid extensions of halfgroupoids and its geometrical meaning