Finite group actions on abelian groups of finite Morley rank

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Borovik, Alexandre
Format: Preprint
Veröffentlicht: 2020
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866916331966693376
author Borovik, Alexandre
author_facet Borovik, Alexandre
contents This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially, these results are needed for the forthcoming work by Ayşe Berkman and myself [5] where we remove the `sharpness' assumption from [4]. Also, they yield a proof of the long standing conjecture of linearity of irreducible definable actions of simple algebraic groups on elementary abelian $p$-groups of finite Morley rank [16, Conjecture 12].
format Preprint
id arxiv_https___arxiv_org_abs_2008_00604
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Finite group actions on abelian groups of finite Morley rank
Borovik, Alexandre
Group Theory
20F11
This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially, these results are needed for the forthcoming work by Ayşe Berkman and myself [5] where we remove the `sharpness' assumption from [4]. Also, they yield a proof of the long standing conjecture of linearity of irreducible definable actions of simple algebraic groups on elementary abelian $p$-groups of finite Morley rank [16, Conjecture 12].
title Finite group actions on abelian groups of finite Morley rank
topic Group Theory
20F11
url https://arxiv.org/abs/2008.00604