Abelian group pairs having a trivial coGalois group

Every Abelian Group Is a Class Group

Let T be the set of minimal primes of a Krull domain A. If S is a subset of T9 we form B = n AP for PeS and study the relation of the class group of B to that of A. We find that the class group of B is always a homomorphic image of that of A. We use this type of construction to obtain a Krull domain with specified class group and then alter such a Krull domain to obtain a Dedekind domain with t...

The trivial group made

Coset enumeration, based on the methods described by Todd & Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such presentation. We show that it is much easier than it rst appears, albeit at the ...

On group Elements Having Square Roots

Proofs for Group and Abelian Group Single Axioms* Proofs for Group and Abelian Group Single Axioms

This memorandum serves as a companion to the paper \Single axioms for groups and Abelian groups with various operations". That paper presents single axioms for groups and Abelian groups in terms of fproduct, inverseg, fdivisiong, fdouble division, identityg, fdouble division, inverseg, fdivision, identityg, and fdivision, inverseg. Proofs that were omitted from that paper are presented here.

A Sharply 2-transitive Group without a Non-trivial Abelian Normal Subgroup

We show that any group G is contained in some sharply 2transitive group G without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups G that we construct have no fixed points.