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Free semigroups of power series
Given power series $f_1,\dots,f_r\in z^2K[[z]]$ over a field of characteristic zero, we show that the semigroup $\langle f_1,\dots,f_r\rangle$ generated by the $f$'s under composition is free of rank $r$ whenever the multiplicative semigroup $\langle\mathrm{lc}(f_1),\dots,\mathrm{lc}(f_r)\rangle$ in
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