converse of lagrange's theorem (clt) numbers under $1000$

converse of lagrange's theorem (clt) numbers under $1000$

a positive integer $n$ is called a clt number if every group of order $n$ satisfies the converse of lagrange's theorem‎. ‎in this note‎, ‎we find all clt and supersolvable numbers up to $1000$‎. ‎we also formulate some questions about the distribution of these numbers‎.

Converse of Lagrange ’ S Theorem ( Clt ) Numbers

A positive integer n is called a CLT number if every group of order n satisfies the converse of Lagrange’s Theorem. In this note, we find all CLT and supersolvable numbers up to 1000. We also formulate some questions about the distribution of these numbers. RÉSUMÉ: Un nombre entier naturel n est appelé nombre CLT si tout groupe d’ordre n satisfait la réciproque du Théorme de Lagrange. Nous déte...

Weil Converse Theorem

Hecke generalized this equivalence, showing that an integral form has an associated Dirichlet series which can be analytically continued to C and satisfies a functional equation. Conversely, Weil showed that, if a Dirichlet series satisfies certain functional equations, then it must be associated to some integral form. Our goal in this paper is to describe this work. In the first three sections...

Ribet’s Converse to Herbrand’s Theorem

A Converse to Dye’s Theorem

Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of F2 on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not univ...

Weil’s converse theorem with poles

We prove a generalization of the classical converse theorem of Weil, allowing the twists by non-trivial Dirichlet characters to have arbitrary poles.