On direct products of generalized solvable groups

On the residual solvability of generalized free products of solvable groups

In this paper, we study the residual solvability of the generalized free product of solvable groups. Dedicated to Laci Babai

Generalized Covering Groups and Direct Limits

Wreath Products and Existentially Complete Solvable Groups

It is known that the theory of abelian groups has a model companion but that the theory of groups does not. We show that for any fixed 22 a 2 the theory of groups solvable of length s 22 has no model companion. For the metabelian case (22 = 2) we prove the stronger result that the classes of finitely generic, infinitely generic, and existentially complete metabelian groups are all distinct. We ...

on direct sums of baer modules

the notion of baer modules was defined recently

on varietal capability of infinite direct products of groups

recently‎, ‎the authors gave some conditions under which a direct product‎ ‎of finitely many groups is $mathcal{v}-$capable if and only if each of its‎ ‎factors is $mathcal{v}-$capable for some varieties $mathcal{v}$‎. ‎in this paper‎, ‎we extend this fact to any infinite direct product of groups‎. ‎moreover‎, ‎we conclude some results for $mathcal{v}-$capability of direct products of infinitel...