"On Subsets and Subgroups Defined by Commutators and Some Related Questions"

The aim of this paper is to survey some results concerning the following subsets of a group G: subsets consisting of commutators, subsets defined by commutators identities, subsets defined by auto- commutators. We are interested in conditions under which each of these sets form a subgroup of G. In particular we continue the inves- tigation started by L.C. Kappe and L.F. Morse on the subset of all commutators in G. Furthermore, we present some recent results concerning the subset of autocommutators in a group and under what conditions these subset forms a subgroup.