Almost-free groups in varieties with torsion (Q579408)

A group G in a variety V of groups is said to be almost free in V if every subgroup of G which can be generated by fewer elements than the cardinality of G is contained in a V-free subgroup of G. In an earlier paper [J. Algebra 91, 36-52 (1984; Zbl 0569.20020)], the author showed that in every torsion-free variety V there is a non-free almost free group of cardinality \(\aleph_ n\) for each positive integer n. Here the same result is established for certain other varieties which may have torsion, namely those varieties which contain some finite non-abelian simple group.