Congruences via Abelian Groups
نویسنده
چکیده
Given a group G acting on a set S, Mobius inversion over the lattice of subgroups can be used to obtain congruences relating the number of elements of S stabilized by each subgroup. By taking S to be a set of subsets, partitions, or permutations congruences for binomial and multinomial coefficients. Stirling numbers of both kinds, and various other combinatorial sequences are derived. Congruences for different moduh are obtained by varying the order of G. m( 1985 Academic ores,
منابع مشابه
Definable principal congruences and solvability
We prove that in a locally finite variety that has definable principal congruences (DPC), solvable congruences are nilpotent, and strongly solvable congruences are strongly abelian. As a corollary of the arguments we obtain that in a congruence modular variety with DPC, every solvable algebra can be decomposed as a direct product of nilpotent algebras of prime power size.
متن کاملAbelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic
We relate the existence of Frobenius morphisms into the Jacobians ofDrinfeldmodular curves to the existence of congruences between cusp forms. Mathematics Subject Classification (2000) Primary 11F33; Secondary 11F52 · 11G10
متن کاملSelmer Groups and the Eisenstein-klingen Ideal
0 Introduction The central point in the Bloch-Kato conjectures is to establish formulas for the order of the Selmer groups attached to Galois representations in terms of the special values of their L-functions. In order to give upper bound, the main way is to construct Euler systems following Kolyvagin. Besides, lower bounds have been obtained by using congruences between automorphic forms. So,...
متن کاملINDUCTIVE CONSTRUCTION OF THE p-ADIC ZETA FUNCTIONS FOR NON-COMMUTATIVE p-EXTENSIONS OF TOTALLY REAL FIELDS WITH EXPONENT p
In this paper, we will construct the p-adic zeta function for a non-commutative p-extension F of a totally real number field F such that the finite part of its Galois group G is a p-group with exponent p. We first calculate the Whitehead groups of the Iwasawa algebra Λ(G) and its canonical Ore localization Λ(G)S by using Oliver-Taylor’s theory on integral logarithms. Then we reduce the main con...
متن کاملProof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases
Fix an odd prime p. Let G be a compact p-adic Lie group containing a closed, normal, pro-p subgroup H which is abelian and such that G/H is isomorphic to the additive group of p-adic integers Zp. First we assume that H is finite and compute the Whitehead group of the Iwasawa algebra, Λ(G), of G. We also prove some results about certain localisation of Λ(G) needed in Iwasawa theory. Let F be a t...
متن کامل