We construct blocks of finite groups with arbitrarily large O-Morita Frobenius numbers. There are no known examples two defined over O, isomorphic defect groups, that not Morita equivalent but the corresponding k are. Therefore, above strongly suggests numbers also unbounded, which would answer a question Benson and Kessar.

‎the frobenius complement of a given frobenius group acts on its kernel‎. ‎the scheme which is arisen from the orbitals of this action is called ferrero pair scheme‎. ‎in this paper‎, ‎we show that the fibers of a ferrero pair scheme consist of exactly one singleton fiber and every two fibers with more than one point have the same cardinality‎. ‎moreover‎, ‎it is shown that the restriction of a...

We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assump tion for the in nite Frobenius elements in the class groups of these orders

Class field theory relates abelian extensions of a given number field K to certain generalized ideal class groups ofK. The fundamental tool for doing this is Frobenius elements, and the Artin map obtained from them. Recall from lecture 24 that if L/K is an abelian extension (i.e., a Galois extension with abelian Galois group), and p is a prime of OK unramified in OL, then we defined Fr(p) ∈ Gal...

We construct an infinite family of representations of finite groups with an irreducible adjoint action and we give an application to the question of lacunary of Frobenius traces in Galois representations. 2010 Mathematics Subject Classification. 11F80, 11R45, 20C15.

Conjectures are given for Hilbert series related to polynomial invariants of finite general linear groups, one for invariants mod Frobenius powers of the irrelevant ideal, one for cofixed spaces of polynomials.

The representation theory of finite groups began with Frobenius's factorization Dedekind's group determinant. In this paper, we consider the case semigroup determinant is nonzero if and only complex algebra Frobenius, so our results include applications to study Frobenius algebras. We explicitly factor for commutative semigroups inverse semigroups. recover Wilf-Lindström a meet semilattice Wood...

We extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, for a finite and totally ramified extension F/Qp, and an arbitrary finite extension K/F , we construct a general class of infinite and totally wildly ramified extensions K∞/K so that the functor V 7→ V |GK∞ is fully-faithfull on the category of F ...

Main mathematical applications of Frobenius manifolds are in the theory of Gromov Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable hierarchies. The theory of Frobenius manifolds establishes remarkable relationships between these, sometimes rather distant, mathematical theo...