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Maximal Divisible Subgroups in Modular Group Rings over a Finite Ring or a Field

Author(s): Peter Danchev

Journal: Boletim da Sociedade Paranaense de Matemática
ISSN 0037-8712

Volume: 29;
Issue: 1;
Start page: 67;
Date: 2011;
Original page

Keywords: abelian groups | divisible subgroups | commutative rings | fields | binomial extensions | normalized units | cardinalities.

We describe up to an isomorphism the algebraic structure of themaximal divisible subgroup dV R[G] of the group V R[G] of normalized units in a group ring R[G], provided that G is an abelian group such that Gt/Gp is (infinite) bounded and R is a field of prime characteristic p. This supplies recent author’s results in Rad. Mat. (2004), Commun. Algebra (2011), Bull. Braz. Math. Soc. (2010) and J. Alg. Numb. Th. Acad. (2010).
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