Displaying similar documents to “Abelian groups with many automorphisms”

Some generalizations of torsion-free Crawley groups

Brendan Goldsmith, Fatemeh Karimi, Ahad Mehdizadeh Aghdam (2013)

Czechoslovak Mathematical Journal

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In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group G is said to be an Erdős group if for any pair of isomorphic pure subgroups H , K with G / H ≅ G / K , there is an automorphism of G mapping H onto K ; it is said to be a weak Crawley group if for any pair H , K of isomorphic dense maximal pure subgroups, there is an automorphism mapping H onto K . We show that these classes are extensive and pay...

The automorphism groups and endomorphism rings of torsion-free abelian groups of rank two

M. Król

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CONTENTS§ 1. Introduction.......................................................................................................................................... 5§ 2. Definitions and lemmas................................................................................................................... 7§ 3. Theorem on the isomorphism of subdirect sums with the same kernels............................. 15§ 4. The group of automorphisms of a torsion-free abelian group of rank two................................

Commutative group algebras of highly torsion-complete abelian p -groups

Peter Vassilev Danchev (2003)

Commentationes Mathematicae Universitatis Carolinae

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A new class of abelian p -groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002).