Thaine's theorem

In mathematics, Thaine's theorem is an analogue of Stickelberger's theorem for real abelian fields, introduced by Thaine (1988).

Thaine's method has been used to shorten the proof of the Mazur–Wiles theorem (Washington 1997), to prove that some Tate–Shafarevich groups are finite, and in the proof of Mihăilescu's theorem (Schoof 2008).

be distinct odd primes with

not dividing

be the Galois group of

ζ

be its group of units, let

be the subgroup of cyclotomic units, and let

be its class group.

annihilates

then it annihilates