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18.4 (2014)

Open

(A. Rhemtulla, S. Sidki).
a) Is a group of the form $G = ABA$ with cyclic subgroups $A$ and $B$ always soluble? (This is known to be true if $G$ is finite.)
b) The same question when in addition $A$ and $B$ are conjugate in $G$.

Contributor: B. Amberg

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