Abstract:
An example of a $2$-generated complete group (different from the identity) with unique extraction of roots is constructed. An example is indicated, in passing, of
a noncyclic $2$-generated group in which every element is conjugate to some power of a fixed element. It is proved that there are continuum many nonisomorphic such examples. The proof is based on a method developed in several papers of A. Yu. Ol'shanskii.
Bibliography: 8 titles.
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