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Reductive homogeneous spaces and nonassociative algebras

Alberto Elduque (2020)

Communications in Mathematics

The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu [Nom54] that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.

Square subgroups of rank two abelian groups

A. M. Aghdam, A. Najafizadeh (2009)

Colloquium Mathematicae

Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.

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