Extensions of Locally Compact Abelian, Torsion-Free Groups by Compact Torsion Abelian Groups
Hossein Sahleh *
Department of Mathematics, University of Guilan, Rasht, Iran.
Ali Akbar Alijani
Ayandegan Collage of Tonekabon, Tonekabon, Iran.
*Author to whom correspondence should be addressed.
Abstract
Let X be a compact torsion abelian group. In this paper, we show that an extension of Fp by X splits where Fpis the p-adic number group and p a prime number. Also, we show that an extension of a torsion-free, non-divisible LCA group by X is not split.
Keywords: Locally compact abelian group, extension, divisible group, torsion-free group