𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Finite Arithmetic Subgroups ofGLn

✍ Scribed by Marcin Mazur

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
134 KB
Volume
75
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

We discuss the following conjecture of Kitaoka:

Here O K is the ring of integers in a finite Galois extension K of Q and K ab is the maximal abelian subextension of K. Our main result reduces this conjecture to a special case of elementary abelian p-groups G. Also, we construct some new examples which negatively answer a question of Y. Kitaoka.

πŸ“œ SIMILAR VOLUMES

Arithmetical definability over finite st
Arithmetical definability over finite structures
✍ Troy Lee πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 134 KB

## Abstract Arithmetical definability has been extensively studied over the natural numbers. In this paper, we take up the study of arithmetical definability over finite structures, motivated by the correspondence between uniform AC^0^ and FO(PLUS, TIMES). We prove finite analogs of three classic r

Automorphisms of Models of True Arithmet
Automorphisms of Models of True Arithmetic: Subgroups which Extend to a Maximal Subgroup Uniquely
✍ Henryk Kotlarski; BoΕΌena Piekart πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 420 KB

## Abstract We show that if __M__ is a countable recursively saturated model of True Arithmetic, then __G__ = Aut(__M__) has nonmaximal open subgroups with unique extension to a maximal subgroup of Aut(__M__). Mathematics Subject Classification: 03C62, 03C50.

Arithmetic of divisibility in finite mod
Arithmetic of divisibility in finite models
✍ Marcin Mostowski; Anna E. Wasilewska πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 110 KB πŸ‘ 1 views

## Abstract We prove that the finite‐model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Ξ ^0^~1~‐complete set of theorems). Additionally we prove FM‐representability theorem for this class of finite models. This means that a relation __R__ on natural nu