Abstract
The following conjecture is investigated: a noncentral subnormal subgroup of the multiplicative group of a division ring contains a noncyclic free subgroup. Special cases are proved, entailing several known commutativity theorems. Also a new framework is presented for some kinds of commutativity theorems, based on the existence of (group) words for which one can always find an appropriate substitution by elements of such a subnormal subgroup that yields a noncentral element. Several families of such words are given; one gets commutativity theorems imposing some restrictions (like periodicity) to the image of these words.
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