= Nottingham group
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{title2=$\mathcal N(\mathbb F_p)$}
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Over $k=\mathbb F_p$, the <Nottingham group> is $\mathcal N(k)=\{f(t)=t+\sum_{i\ge2}a_it^i:a_i\in k\}$ with composition and the $t$-adic <topology>. Equivalently it is the <group> of continuous $k$-automorphisms of the <Laurent series field> $k((t))$ that act trivially on $(t)/(t^2)$. With ordinary series composition, the <isomorphism> sends $f$ to the automorphism $h(t)\mapsto h(f^{-1}(t))$; this inverse avoids reversing the <group> product. It is a <pro-p group>, recovered from its finite truncations, and contains elements of arbitrarily large finite $p$-power order.
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