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>See also
>ramification group
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Ramification group
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In number theory, more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives detailed information on the ramification phenomena of the extension.
Contents
1 Ramification groups in lower numbering
1.1 Example: the cyclotomic extension
1.2 Example: a quartic extension
2 Ramification groups in upper numbering
2.1 Herbrand's theorem
3 See also
4 Notes
5 References
Example: the cyclotomic extension
The ramification groups for a cyclotomic extension {\displaystyle K_{n}:=\mathbf {Q} _{p}(\zeta )/\mathbf {Q} _{p}}{\displaystyle K_{n}:=\mathbf {Q} _{p}(\zeta )/\mathbf {Q} _{p}}, where {\displaystyle \zeta }\zeta is a