Nottingham group

2020 Mathematics Subject Classification: Primary: 20E18 [MSN][ZBL]

The subgroup of automorphisms of the field of formal power series $\mathbf{F_p}[[t]]$ consisting of those automorphisms of the form $f(t) \mapsto f(g(t))$ where $g(t) \in t + O(t^2)$.

It is a finitely generated, just infinite pro-$p$ group of finite width. However, every separable pro-$p$ group can be embedded in it as a closed subgroup.

References

• Rachel D. Camina, "Subgroups of the Nottingham group" J. Algebra 196 (1997) 101-113 Zbl 0883.20015