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Abelian groups of zero adjoint entropy

L. Salce, P. Zanardo (2010)

Colloquium Mathematicae

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 ideals of a Borel subalgebra and root systems

Dmitri I. Panyushev (2014)

Journal of the European Mathematical Society

Let 𝔤 be a simple Lie algebra and 𝔄𝔟 o the poset of non-trivial abelian ideals of a fixed Borel subalgebra of 𝔤 . In [8], we constructed a partition 𝔄𝔟 o = ⊔ μ 𝔄𝔟 μ parameterised by the long positive roots of 𝔤 and studied the subposets 𝔄𝔟 μ . 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 𝔤 is a join-semilattice.

Abelian pro-countable groups and orbit equivalence relations

Maciej Malicki (2016)

Fundamenta Mathematicae

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 quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let G be any group and let A be an abelian quasinormal subgroup of G . If n is any positive integer, either odd or divisible by 4 , then we prove that the subgroup A n is also quasinormal in G .

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