This book provides a comprehensive exposition of the use of set-theoretic methods in
abelian group theory, module theory, and homological algebra, including applications to …

Let V denote a variety of algebras in a countable language. An algebra is said to be L∞ κ-
free if it is L∞ κ-equivalent to a (V-) free algebra. If every L∞ ω1-free algebra of cardinality ω …

Let V be a non-trivial variety of groups. For every 0< n< ω, V has a non-free ℵ n-free group of
cardinality ℵ n if and only V is not a variety of nilpotent groups of prime power exponent. If V …

In [11] Sklinos proved that any uncountable free group is not $\aleph_1 $-homogenenous.
This was later generalized by Belegradek in [1] to torsion-free residually finite relatively free …

Under the assumption of the axiom of constructibility of set theory it is shown that for varieties
of groups of exponent zero and for uncountable, regular, not weakly compact cardinals k …

Let V be a variety of groups. A group G is said to be almost V-free if every subgroup of G that
can be generated by fewer elements than the cardinality of G is contained in a V-free …

В предположении аксиомы $\Delta_k $ для любого несчетного регулярного кардинала $
k $ и многообразия групп $ V $ нулевой экспоненты, свободные группы которого …

Основной целью настоящей работы является изучение почти свободных групп
бесконечных мощностей в многообразиях групп© нулевой экспоненты. А именно, будет …

In the paper the structure is analyzed of almost free groups (of infinite cardinalities k) in
arbitrary varieties of groups containing the variety of all abelian groups~. In [i] it was shown …

In this paper we are concerned with a variety V of groups of exponent zero (ie, with a variety
containing the variety 92 of all abellan groups). Namely, we focus on infinite groups that are …