Nottingham group
Encyclopedia
In the mathematical
field of group theory
, the Nottingham group is the group J(Fp) or N(Fp) consisting of formal power series t + a2t2+...
with coefficients in Fp. The group multiplication is given by formal composition also called substitution. That is, if
and if
is another element, then
.
Notably, the group multiplication is not abelian
. The group was studied by and the name "Nottingham group" refers to Johnson's former domicile. It is a finitely generated pro-p-group.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
field of group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
, the Nottingham group is the group J(Fp) or N(Fp) consisting of formal power series t + a2t2+...
with coefficients in Fp. The group multiplication is given by formal composition also called substitution. That is, if
and if
is another element, then.Notably, the group multiplication is not abelian
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order . Abelian groups generalize the arithmetic of addition of integers...
. The group was studied by and the name "Nottingham group" refers to Johnson's former domicile. It is a finitely generated pro-p-group.