Displaying similar documents to “A note on the isomorphism of modular group algebras of p -mixed Abelian groups with divisible p -components.”

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...

Commutative group algebras of highly torsion-complete abelian p -groups

Peter Vassilev Danchev (2003)

Commentationes Mathematicae Universitatis Carolinae

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A new class of abelian p -groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002).

Warfield invariants in abelian group rings.

Peter V. Danchev (2005)

Extracta Mathematicae

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Let R be a perfect commutative unital ring without zero divisors of (R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.

Group algebras of abelian groups

Donna Beers, Fred Richman, Elbert A. Walker (1983)

Rendiconti del Seminario Matematico della Università di Padova

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Isomorphism of commutative group algebras of p -mixed splitting groups over rings of characteristic zero

Peter Vassilev Danchev (2006)

Mathematica Bohemica

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Suppose G is a p -mixed splitting abelian group and R is a commutative unitary ring of zero characteristic such that the prime number p satisfies p ∉ inv ( R ) ∪ zd ( R ) . Then R ( H ) and R ( G ) are canonically isomorphic R -group algebras for any group H precisely when H and G are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).