Nearly Supersolvable Groups and Applications to Artin L-functions
نویسنده
چکیده
In this note, we apply the group-theoretic method to study Artin’s conjecture, and introduce the notations of nearly nilpotent groups and nearly supersolvable groups to answer of a question of Arthur and Clozel. As an application, we show that Artin’s conjecture is valid for all nearly supersolvable Galois extensions of number fields as well as all solvable Frobenius extensions.
منابع مشابه
Rational permutation modules for finite groups
By the Artin Induction theorem,C(G) is a finite abelian group with exponent dividing the order of G. Some work on this sequence has already been done. In [14] and [16], Ritter and Segal proved that C(G) = 0 for G a finite p–group. Serre [17, p. 104] remarked that C(G) / = 0 for G = Z/3 × Q8 (the direct product of a cyclic group of order 3 and a quaternion group of order 8). Berz [2] gave a nice...
متن کاملUniversal Upper Bound for the Growth of Artin Monoids
In this paper we study the growth rates of Artin monoids and we show that 4 is a universal upper bound. We also show that the generating functions of the associated right-angled Artin monoids are given by families of Chebyshev polynomials. Applications to Artin groups and positive braids are given.
متن کاملOn p-adic Artin L-functions II
Let p be a prime. Iwasawa’s famous conjecture relating Kubota-Leopoldt p-adic L-functions to the structure of certain Galois groups has been proven by Mazur and Wiles in [10]. Wiles later proved a far-reaching generalization involving p-adic L-functions for Hecke characters of finite order for a totally real number field in [14]. As we discussed in [5], an analogue of Iwasawa’s conjecture for p...
متن کاملIntroduction to the Langlands Program
This article is an introduction to automorphic forms on the adeles of a linear reductive group over a number field. The first half is a summary of aspects of local and global class field theory, with emphasis on the local Weil group, the L functions of Artin and Hecke, and the role of Artin reciprocity in relating the two kinds of L functions. The first half serves as background for the second ...
متن کاملON THE p-ADIC STARK CONJECTURE AT s = 1 AND APPLICATIONS
Let E/F be a finite Galois extension of totally real number fields and let p be a prime. The ‘p-adic Stark conjecture at s = 1’ relates the leading terms at s = 1 of p-adic Artin L-functions to those of the complex Artin L-functions attached to E/F . We prove this conjecture unconditionally when E/Q is abelian. Moreover, we also show that for certain non-abelian extensions E/F the p-adic Stark ...
متن کامل