1.47 (1965)
SolvedA subgroup $H$ of a group $G$ is said to be strictly isolated if, whenever $x g_1^{-1} x g_1 \dots g_n^{-1} x g_n$ belongs to $H$, so do $x$ and each $g_i^{-1} x g_i$. A group in which the identity subgroup is strictly isolated is called an $S$-group. Do there exist $S$-groups that are not orderable groups?
Progress
Yes, such groups do exist (V. V. Bludov, Algebra and Logic, 13 (1974), 343–360).
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