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A Hajós type result on factoring finite abelian groups by subsets. II

Keresztély Corrádi, Sándor Szabó (2010)

Commentationes Mathematicae Universitatis Carolinae

It is proved that if a finite abelian group is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be periodic. This result generalizes Hajós's factorization theorem.

A note on a theorem of Megibben

Peter Vassilev Danchev, Patrick Keef (2008)

Archivum Mathematicum

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.

A note on group algebras of p -primary abelian groups

William Ullery (1995)

Commentationes Mathematicae Universitatis Carolinae

Suppose p is a prime number and R is a commutative ring with unity of characteristic 0 in which p is not a unit. Assume that G and H are p -primary abelian groups such that the respective group algebras R G and R H are R -isomorphic. Under certain restrictions on the ideal structure of R , it is shown that G and H are isomorphic.

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