Let $H$ be any connected subgroup of a matrix group $G$. Show that $S = \bigcup_{x \in G} xHx^{-1}$ is connected.
2026-03-29 21:14:49.1774818889
Union of conjugates of a connected subgroup of a matrix group is connected.
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Hint: if a family of connected sets has a common element, the union of these connected sets must be connected.