Displaying similar documents to “Square subgroups of rank two abelian groups”

Abelian groups have/are near Frattini subgroups

Simion Breaz, Grigore Călugăreanu (2002)

Commentationes Mathematicae Universitatis Carolinae

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The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.

A Note on Additive Groups of Some Specific Associative Rings

Mateusz Woronowicz (2016)

Annales Mathematicae Silesianae

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Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.

Direct decompositions and basic subgroups in commutative group rings

Peter Vassilev Danchev (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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An attractive interplay between the direct decompositions and the explicit form of basic subgroups in group rings of abelian groups over a commutative unitary ring are established. In particular, as a consequence, we give a simpler confirmation of a more general version of our recent result in this aspect published in Czechoslovak Math. J. (2006).