Displaying similar documents to “A note on clean abelian groups”

Sylow P-Subgroups of Abelian Group Rings

Danchev, P. (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34. Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the...

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.

Isomorphism of Commutative Modular Group Algebras

Danchev, P. (1997)

Serdica Mathematical Journal

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∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91. Let K be a field of characteristic p > 0 and let G be a direct sum of cyclic groups, such that its torsion part is a p-group. If there exists a K-isomorphism KH ∼= KG for some group H, then it is shown that H ∼= G. Let G be a direct sum of cyclic groups, a divisible group or a simply presented torsion abelian group. Then...

A note on a theorem of Megibben

Peter Vassilev Danchev, Patrick Keef (2008)

Archivum Mathematicum

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We prove that pure subgroups of thick Abelian p -groups which are modulo countable are again thick. This generalizes a result due to Megibben (Michigan Math. J. 1966). Some related results are also established.