Unbounded direct sums of cyclic p-groups are characteristically inert socle-regular groups [Articol]

Abstract

It was proved by Chekhlov-Danchev in Commun. Algebra (2022) that unbounded direct sums of cyclic p-groups are (weakly) characteristically inert socle-regular for any prime p. This short note aims to give a new more direct and transparent proof of this fact, provided the prime number p is odd, that is, different to 2.