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A characterization of subgroup lattices of finite abelian groups.

Herrmann, Christian, Takách, Géza (2005)

Beiträge zur Algebra und Geometrie

A direct factor theorem for commutative group algebras

William Ullery (1992)

Commentationes Mathematicae Universitatis Carolinae

Suppose $F$ is a field of characteristic $p \neq 0$ and $H$ is a $p$ -primary abelian $A$ -group. It is shown that $H$ is a direct factor of the group of units of the group algebra $F H$ .

A generalization of a theorem of F. Richman and C. P. Walker

Jindřich Bečvář (1982)

Rendiconti del Seminario Matematico della Università di Padova

A Multiplication Theorem for Strong Starters.

Kenneth B. Gross (1974)

Aequationes mathematicae

A Multiplication Theorem for Strong Starters. (Short Communication).

Kenneth B. Gross (1974)

Aequationes mathematicae

A new proof of Prüfer's theorem

Robert El Bashir (1993)

Acta Universitatis Carolinae. Mathematica et Physica

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 clean abelian groups

Brendan Goldsmith, Peter Vámos (2007)

Rendiconti del Seminario Matematico della Università di Padova

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.

A note on isomorphic commutative group algebras over certain rings.

Danchev, Peter (2005)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

A note on the countable extensions of separable $p^{ω + n}$ -projective abelian $p$ -groups

Peter Vassilev Danchev (2006)

Archivum Mathematicum

It is proved that if $G$ is a pure $p^{ω + n}$ -projective subgroup of the separable abelian $p$ -group $A$ for $n \in N \cup {0}$ such that $| A / G | \leq ℵ_{0}$ , then $A$ is $p^{ω + n}$ -projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005).

Abelian groups in a topos of sheaves: Torsion and essential extensions.

Bhutani, Kiran R. (1989)

International Journal of Mathematics and Mathematical Sciences

Abelian groups with anti-isomorphic endomorphism rings

G. D'Este (1978)

Rendiconti del Seminario Matematico della Università di Padova

Abelian torsion groups with artinian primary components and their automorphisms

Jutta Hausen (1971)

Fundamenta Mathematicae

Almost coproducts of finite cyclic groups

Paul Hill (1995)

Commentationes Mathematicae Universitatis Carolinae

A new class of $p$ -primary abelian groups that are Hausdorff in the $p$ -adic topology and that generalize direct sums of cyclic groups are studied. We call this new class of groups almost coproducts of cyclic groups. These groups are defined in terms of a modified axiom 3 system, and it is observed that such groups appear naturally. For example, $V (G) / G$ is almost a coproduct of finite cyclic groups whenever $G$ is a Hausdorff $p$ -primary group and $V (G)$ is the group of normalized units of the modular group algebra...

Almost totally projective groups

Paul Hill, William Ullery (1996)

Czechoslovak Mathematical Journal

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