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8.8 (1982)

Partially Solved

(D. V. Anosov).
a) Does there exist a non-cyclic finitely-generated group $G$ containing an element $a$ such that every element of $G$ is conjugate to a power of $a$?
b) Does there exist a non-cyclic finitely presented group $G$ which contains an element $a$ such that each element of $G$ is conjugate to some power of $a$?

Contributor: R. I. Grigorchuk

Progress

a) Yes, there does (V. S. Guba, Math. USSR–Izv., 29 (1986), 233–277).

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