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We prove that if $G$ is an abelian $p$ -group with a nice subgroup $A$ so that $G / A$ is a $Σ$ -group, then $G$ is a $Σ$ -group if and only if $A$ is a $Σ$ -subgroup in $G$ provided that $A$ is equipped with a valuation induced by the restricted height function on $G$ . In particular, if in addition $A$ is pure in $G$ , $G$ is a $Σ$ -group precisely when $A$ is a $Σ$ -group. This extends the classical Dieudonné criterion (Portugal. Math., 1952) as well as it supplies our recent results in (Arch. Math. Brno, 2005), (Bull. Math. Soc. Sc. Math....

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Tensor product and quasi-splitting of Abelian groups

The Balance of Tor.

The Burnside Ring of a Cyclic Extension of a Torus.

The $\oplus_{c}$ -topology is not completable

The $\oplus_{c}$ -topology on abelian $p$ -groups

The Cayley graphs of $ℤ^{d}$ and the limits of vertex-primitive graphs of $H A$ -type.

The conjugacy-vectors of all relative holomorphs of an elementary Abelian group of order 16

The construction of $A$ -solvable Abelian groups

The duality theorem for locally compact Abelian $n$ -groups.

The elementary theory of Abelian groups with m-chains of pure subgroups

The Erdős-Ginzburg-Ziv theorem in Abelian non-cyclic groups.

The Extension Theory of the Symmetric and Alternating Groups.

The Functor Bext under the Negation of CH.

The generalized criterion of Dieudonné for primary valuated groups

The generalized criterion of Dieudonné for valuated $p$ -groups

The geometry of the set of characters iduced by valuations.

The graph of generating sets of an abelian group

The group of homomorphisms of Abelian torsion groups.

The homological dimension of a torsion-free abelian group of finite rank as a module over its ring of endomorphisms

The Homological Dimension of an Abelian Group as a Module over its Ring of Endomorphisms. III.

Currently displaying 1 – 20 of 44