 Nottingham group

Over $k={\mathbb{F}}_p$, the Nottingham group is $\mathcal{N}(k)=\{f(t)=t+{\sum }_{i\ge 2}{a}_i{t}^i:a_i\in k\}$ 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.

The Nottingham Group refers to a research consortium or collective of researchers based at the University of Nottingham, primarily focusing on various fields such as health, education, and social sciences. The group often collaborates on projects related to public health, clinical research, and innovations in education, among other areas. One of the notable subsets associated with the Nottingham Group is the **Nottingham University Hospitals NHS Trust**, which collaborates with the university for clinical research and advancements in healthcare.