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Displaying similar documents to “On free subgroups of units in quaternion algebras”

On free subgroups of units in quaternion algebras II

Jan Krempa (2003)

Colloquium Mathematicae

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Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.

Square subgroups of rank two abelian groups

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

Colloquium Mathematicae

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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.