We study the index of the group of units in the genus field of an imaginary quadratic number field modulo the subgroup generated by the units of the quadratic subfields (over ‫)ޑ‬ of the genus field.

The main problem when solving a Thue equation is the computation of the unit group of a certain number field. In this paper we show that the knowledge of a subgroup of finite index is actually sufficient. Two examples linked with the primitive divisor problem for Lucas and Lehmer sequences are given.

In this short note we prove that any irreducible algebraic monoid whose unit group is an affine algebraic group is affine.

The Chazy, Black River and Trenton Groups are a well studied sequence of fossiliferous limestones, dolostones and sandstones in the Champlain Valley of New York, Vermont and southern Quebec. These rocks record shallow water cyclic sedimentation in the foreland basin of Laurentia prior to and during the initial stages of the Taconic Orogeny. This field trip reviews the stratigraphy of these unit...

in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

In this article we construct free groups and subgroups of finite index in the unit group of the integral group ring of a finite non-abelian group G for which every non-linear irreducible complex representation is of degree 2 and with commutator subgroup G′ a central elementary abelian 2-group.

Let KG denote the group algebra of the group G over the field K and let U(KG) denote its group of units. Here without the use of a computer we give presentations for the unit groups of all group algebras KG, where the size of KG is less than 1024. As a consequence we find the minimum counterexample to the Isomorphism Problem for group algebras. AMS Subject Classification: 16S34, 16U60, 20C05

Number fields and global function fields have many similar properties. Both have many applications to cryptography and coding theory, and the main computational problems for number fields, such as computing the ring of integers and computing the class group and the unit group, have analogues over function fields. The complexity of the number field problems has been studied extensively and these...

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of the group G. MSC2000: Primary 16S34, 20C05; Secondary 16U60