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Generalized Dieudonné criterion.

Danchev, P. — 2005

Acta Mathematica Universitatis Comenianae. New Series

Isomorphism of Commutative Modular Group Algebras

Danchev, P. — 1997

Serdica Mathematical Journal

∗ 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 KH ∼= KG as...

Sylow P-Subgroups of Abelian Group Rings

Danchev, P. — 2003

Serdica Mathematical Journal

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 present work,...

Trivial units in commutative group algebras.

P. Danchev — 2008

Extracta Mathematicae

Ulm-Kaplansky invariants of S(KG)/G

P. V. Danchev — 2005

Bulletin of the Polish Academy of Sciences. Mathematics

Let G be an infinite abelian p-group and let K be a field of the first kind with respect to p of characteristic different from p such that $s_{p} (K) = ℕ$ or $s_{p} (K) = ℕ \cup 0$ . The main result of the paper is the computation of the Ulm-Kaplansky functions of the factor group S(KG)/G of the normalized Sylow p-subgroup S(KG) in the group ring KG modulo G. We also characterize the basic subgroups of S(KG)/G by proving that they are isomorphic to S(KB)/B, where B is a basic subgroup of G.

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