Abelian groups in which every pure subgroup is an isotype subgroup
Abelian groups in which every -isotype subgroup is a pure subgroup, resp. an isotype subgroup
Abelian groups of zero adjoint entropy
The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint...
Abelian groups that cannot be factored without periodic factor
Abelian groups which have trivial absolute coGalois group
In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.
Abelian groups whose endomorphism ring is linearly compact
Abelian Groups with an Endomorphism with Irreducible minimum Polynomial
Abelian groups with anti-isomorphic endomorphism rings
Abelian groups with many automorphisms
Abelian ideals of a Borel subalgebra and root systems
Let be a simple Lie algebra and the poset of non-trivial abelian ideals of a fixed Borel subalgebra of . In [8], we constructed a partition parameterised by the long positive roots of and studied the subposets . In this note, we show that this partition is compatible with intersections, relate it to the Kostant-Peterson parameterisation and to the centralisers of abelian ideals. We also prove that the poset of positive roots of is a join-semilattice.
Abelian Normal Subgroups of M-Groups.
Abelian p-adic Group Rings.
Abelian pro-countable groups and orbit equivalence relations
We study a class of abelian groups that can be defined as Polish pro-countable groups, as non-archimedean groups with a compatible two-sided invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable discrete groups, endowed with the product topology. We show that for every non-locally compact, abelian quasi-countable group G there exists a closed L ≤ G and a closed, non-locally compact K ≤ G/L which is a direct product of discrete countable groups....
Abelian profinite groups
Abelian quasinormal subgroups of groups
Let be any group and let be an abelian quasinormal subgroup of . If is any positive integer, either odd or divisible by , then we prove that the subgroup is also quasinormal in .
Abelian subgroup separability of some one-relator groups.
Abelian subgroups of polycyclic groups.
Abelian subgroups of the Torelli group.
Abelian torsion groups with a pseudocompact group topology.
Abelian torsion groups with artinian primary components and their automorphisms