Minus class groups of the fields of the l-th roots of unity
نویسنده
چکیده
Abstract. We show that for any prime number l > 2 the minus class group of the field of the l-th roots of unity Qp(ζl) admits a finite free resolution of length 1 as a module over the ring Ẑ[G]/(1 + ι). Here ι denotes complex conjugation in G = Gal(Qp(ζl)/Qp) ∼= (Z/lZ)∗. Moreover, for the primes l ≤ 509 we show that the minus class group is cyclic as a module over this ring. For these primes we also determine the structure of the minus class group.
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ورودعنوان ژورنال:
- Math. Comput.
دوره 67 شماره
صفحات -
تاریخ انتشار 1998