Vol. 1, No. 1, 2022

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Groups of finite Morley rank with a generically multiply transitive action on an abelian group

Ayşe Berkman and Alexandre Borovik

Vol. 1 (2022), No. 1, 1–14
DOI: 10.2140/mt.2022.1.1
Abstract

We investigate the configuration where a group of finite Morley rank acts definably and generically m-transitively on an elementary abelian p-group of Morley rank n, where p is an odd prime, and m n. We conclude that m = n, and the action is equivalent to the natural action of GL n(F) on Fn for some algebraically closed field F. This strengthens one of our earlier results, and partially answers two problems posed by Borovik and Cherlin in 2008.

Keywords
groups of finite Morley rank, generically transitive actions
Mathematical Subject Classification
Primary: 03C60, 20F11
Milestones
Received: 22 July 2021
Revised: 14 December 2021
Accepted: 9 February 2022
Published: 24 June 2022
Authors
Ayşe Berkman
Mathematics Department
Mimar Sinan Fine Arts University
Istanbul
Turkey
Alexandre Borovik
Department of Mathematics
University of Manchester
United Kingdom