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486:, and Chapter 16 "Thaine's Theorem" (pp. 107â115) for proof of a special case of Thaine's theorem.
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See in particular
Chapter 14 (pp. 91â94) for the use of Thaine's theorem to prove
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564:) for Thaine's theorem (section 15.2) and its application to the
31:). Thaine's method has been used to shorten the proof of the
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493:"On the ideal class groups of real abelian number fields"
463:, Universitext, London: Springer-Verlag London, Ltd.,
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for real abelian fields, introduced by Thaine (
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214:{\displaystyle F=\mathbb {Q} (\zeta _{p}^{+})}
283:be the subgroup of cyclotomic units, and let
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350:{\displaystyle \theta \in \mathbb {Z} }
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587:Theorems in algebraic number theory
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539:Introduction to Cyclotomic Fields
43:are finite, and in the proof of
560:See in particular Chapter 15 (
439:{\displaystyle Cl^{+}/Cl^{+q}}
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331:
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1:
236:{\displaystyle \mathbb {Q} }
99:be distinct odd primes with
263:be its group of units, let
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490:Thaine, Francisco (1988),
388:{\displaystyle E/CE^{q}}
535:Washington, Lawrence C.
313:be its class group. If
172:be the Galois group of
41:TateâShafarevich groups
25:Stickelberger's theorem
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306:{\displaystyle Cl^{+}}
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165:{\displaystyle G^{+}}
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484:MihÄilescu's theorem
461:Catalan's conjecture
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395:then it annihilates
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45:MihÄilescu's theorem
566:MazurâWiles theorem
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138:{\displaystyle p-1}
33:MazurâWiles theorem
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23:is an analogue of
582:Cyclotomic fields
470:978-1-84800-184-8
276:{\displaystyle C}
256:{\displaystyle E}
112:{\displaystyle q}
92:{\displaystyle q}
72:{\displaystyle p}
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19:In mathematics,
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502:, 2nd ser.,
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457:Schoof, René
357:annihilates
58:
20:
18:
506:(1): 1â18,
55:Formulation
49:Schoof 2008
576:Categories
450:References
324:∈
321:θ
195:ζ
130:−
537:(1997),
459:(2008),
557:1421575
528:0951505
520:1971460
479:2459823
555:
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243:, let
145:. Let
516:JSTOR
221:over
543:ISBN
465:ISBN
79:and
59:Let
29:1988
508:doi
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