Abelian groups

Commuting self-adjoint partial differential operators and a group theoretic problem

/pdf/a-torsion-theory-for-abelian-categories-5asiqzwtbm.pdf

A torsion theory for Abelian categories

We solve here some problems from Fuchs’ book. We show that the answer to Whitehead’s problem (for groups of power ℵ1) is independent from the usual axioms of set theory. We prove the existence of large rigid systems for groups of power λ, with no restriction on λ. We also prove that there are many non-isomorphic reduced separablep-groups.

Infinite abelian groups, whitehead problem and some constructions

A group is said to have the property T or to be a T-group if every subnormal subgroup is normal. Thus the class of T-groups is just the class of all groups in which normality is a transitive relation. Finite T-groups have been studied by Best and Taussky (l), Gaschutz (4) and Zacher (11). Gaschutz has shown that if G is a finite soluble T-group and G/L is the unique maximal nilpotent quotient group of G, then G/L is Abelian or Hamiltonian and L is an Abelian group of odd order prime to |G:L| ((4), Satz 1). Our aim is to study infinite T-groups and more especially infinite soluble T-groups with a view to extending Gaschutz's results. One of the simplest results on soluble T-groups is THEOREM 2.3.1. Every soluble T-group is metabelian.

Groups in which normality is a transitive relation

/pdf/refinements-for-infinite-direct-decompositions-of-algebraic-211mfqyawc.pdf

Abelian groups

Citations

Commuting self-adjoint partial differential operators and a group theoretic problem

A torsion theory for Abelian categories

Infinite abelian groups, whitehead problem and some constructions

Groups in which normality is a transitive relation

Refinements for infinite direct decompositions of algebraic systems.

Related Papers (5)

Infinite Abelian groups

Every Countable Reduced Torsion-Free Ring is an Endomorphism Ring

Abstract Harmonic Analysis

Structure of rings

Abelian groups without elements of finite order