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

Abstract

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).

Keywords

• abelian groups
• divisible subgroups
• commutative rings
• fields
• binomial extensions
• normalized units
• cardinalities.