Nottingham group

In the mathematical field of group theory, the Nottingham group is the group J(F_p) or N(F_p) consisting of formal power series t + a₂t²+... with coefficients in F_p. The group multiplication is given by formal composition also called substitution. That is, if

$f = t+ \sum_{n=2}^\infty a_n t^n$

and if g is another element, then

$gf = f(g) = g+ \sum_{n=2}^\infty a_n g^n$.

Notably, the group multiplication is not abelian. The group was studied by Johnson (1988) and the name "Nottingham group" refers to Johnson's former domicile. It is a finitely generated pro-p-group.

See also

• Fesenko group

References

• Camina, Rachel (2000), "The Nottingham group", in Sautoy, Marcus Du; Segal, Dan; Shalev, Aner, New horizons in pro-p groups, Progr. Math., 184, Boston, MA: Birkhäuser Boston, pp. 205–221, ISBN 978-0-8176-4171-9, MR1765121, http://books.google.com/books?isbn=0817641718 
• Johnson, D. L. (1988), "The group of formal power series under substitution", Australian Mathematical Society. Journal. Series A. Pure Mathematics and Statistics 45 (3): 296–302, ISSN 0263-6115, MR957195, http://anziamj.austms.org.au/JAMSA/V45/Part3/Johnson.html