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Ayse Berkman

Publications and source records attributed to Ayse Berkman.

3 recordsLinked to original sources
arXiv2018

Sharply 2-transitive groups of finite Morley rank

A sharply 2-transitive permutation group of finite Morley rank and characteristic 2 splits; a split sharply 2-transitive permutation group of finite Morley rank and characteristic different from 2 is the group of affine transformations of an algebraically closed field. In particular, a sharply 2-transitive permutation group of finite Morley rank of characteristic 3 is the group of affine transformations of an algebraically closed field of characteristic 3. Without any assumption on Morley rank, a sharply 2-transitive permutation group of characteristic 0 splits if its point stabilizers are virtually abelian.

math.LO↗
arXiv2011

Groups of Finite Morley Rank with a Pseudoreflection Action

In this work, we give two characterisations of the general linear group as a group $G$ of finite Morley rank acting on an abelian connected group $V$ of finite Morley rank definably, faithfully and irreducibly. To be more precise, we prove that if the pseudoreflection rank of $G$ is equal to the Morley rank of $V$, then $V$ has a vector space structure over an algebraically closed field, $G\cong GL(V)$ and the action is the natural action. The same result holds also under the assumption of Prufer 2-rank of $G$ being equal to the Morley rank of $V$.

math.GR↗