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To embed the bouquet of $g$ circles $B_g$ into the $n$-sphere $S^n$ so thatits full symmetry group action extends to an orthogonal actions on $S^n$, theminimal $n$ is $2g-1$. This answers a question raised by B. Zimmermann.

The minimal dimension of a sphere with an equivariant embedding of the bouquet of $g$ circles is $2g-1$