Groups of finite Morley rank with a generically multiply transitive action on an abelian group
Model theory, 2022 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 $m\geqslant n$. We conclude that $m=n$, and the action is equivalent to the natural action of $\operatorname{GL}_n(F)$ on $F^n$ for some algebraically ...
Alexandre V Borovik
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Groups of finite Morley rank with a generically sharply multiply transitive action [PDF]
Journal of Algebra, 2018 We prove that if $G$ is a group of finite Morley rank which acts definably and generically sharply $n$-transitively on a connected abelian group $V$ of Morley rank $n$ with no involutions, then there is an algebraically closed field $F$ of characteristic $\ne 2$ such that $V$ has a structure of a vector space of dimension $n$ over $F$ and $G$ acts on ...
Alexandre V Borovik
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Normal subgroups of finite multiply transitive permutation groups [PDF]
Nagoya Mathematical Journal, 1974 Wagner [5] and Ito [2] proved the following theorems respectively.THEOREM OF WAGNER. Let G be a triply transitive permutation group on a set Ω = {1,2, …, n}, and let n be odd and n > 4. If H is a normal subgroup (≠1) of G, then H is also triply transitive on Ω.
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Conjugacy Classes of Involutions in the Group of Homeomorphisms of the Rational Numbers
, 2001 Let X be the set of real rational numbers Q with the topology induced by the usual topology on R and let AutX be the set of functions f : X → X which are homeomorphisms with respect to this topology.
Bruyns, PV
core
On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups. [PDF]
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Discovering Noncritical Organization: Statistical Mechanical, Information Theoretic, and Computational Views of Patterns in One-Dimensional Spin Systems. [PDF]
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