Weakly fully and characteristically inert socle-regular Abelian p-groups

Abstract

In regard to two recent publications in the Mediterranean J. Math. (2021) and Forum Math. (2021) related to fully and characteristically inert socleregularity, respectively, we define and study the so-called weakly characteristically inert socle-regular groups. In that aspect, as a culmination of the investigations of this sort, some more global results are obtained and, moreover, some new concrete results concerning the weakly fully inert socle-regular groups, defined as in the firstly mentioned above paper, are also established. In particular, we prove that all torsion-complete groups are characteristically inert socle-regular, which encompasses an achievement from the secondly mentioned paper and completely settles the problem posed there about this class of groups