相关论文: Groups of finite Morley rank with a generically mu…

In this paper we show that the natural action of the symmetric group acting on the product space $\{0, 1 \}^{\mathbb{N}} $ endowed with a symmetric measure is approximately transitive. We also extend the result to a larger class of…

We study definably primitive pseudo-finite permutation groups of finite $SU$-rank. We show that if $(G,X)$ is such a permutation group, then the rank of $G$ can be bounded in terms of the rank of $X$, providing an analogue of a theorem of…

Suppose $\mathbb{F}$ is a field of prime characteristic $p$ and $E$ is a finite subgroup of the additive group $(\mathbb{F},+)$. Then $E$ is an elementary abelian $p$-group. We consider two such subgroups, say $E$ and $E'$, to be equivalent…

We give an algebraic description of the structure of the analytic universal cover of a complex abelian variety which suffices to determine the structure up to isomorphism. More generally, we classify the models of theories of "universal…

Let $\F_q$ be the finite field with $q$ elements, $p=\Char \F_q$. The group $\GL_2(\F_q)$ acts naturally in the set of irreducible polynomials over $\F_q$ of degree at least $2$. In this paper we are interested in the characterization and…

We prove that if the group of fixed points of a generic automorphism of a simple group of finite Morley rank is pseudofinite, then this group is an extension of a (twisted) Chevalley group over a pseudofinite field. On the way to obtain…

We prove global rigidity results for some linear abelian actions on tori. The type of actions we deal with includes in particular maximal rank semisimple actions on $\T^N$.

Let $p$ be a prime number. A longstanding conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we prove that if $G$ is an odd order finite non-abelian monolithic $p$-group such…

Let $G$ be a permutation group acting on a finite set $\Omega$ of cardinality $n$. The number of orbits of the induced action of $G$ on the set $\Omega_m$ of all size $m$ subsets of $\Omega$ satisfies the trivial inequalities…

Let $G$ be a finite group and assume $p$ is a prime dividing the order of $G$. Suppose for any such $p$, that every two abelian $p$-subgroups of $G$ of equal order are conjugate. The structure of such a group $G$ has been settled in this…

It is shown, from $\sigma$-centered Martin's Axiom, that there exists a proper dense subgroup of the symmetric group on a countably infinite set whose natural action on sufficiently flexible relational structures is transitive. This allows…

Let M be a closed, connected, orientable topological 4-manifold, and G be a finite group acting topologically and locally linearly on M. In this paper we investigate the Borel spectral sequence for the G-equivariant cohomology of M, and…

This paper contains the more significant part of the article with the same title that will appear in the Volume 12 of Journal of Group Theory (2009). In this paper we determine all algebraic transformation groups $G$, defined over an…

The generalized Mordell-Lang conjecture (GML) is the statement that the irreducible components of the Zariski closure of a subset of a group of finite rank inside a semi-abelian variety are translates of closed algebraic subgroups. M.…

Originally motivated by questions of P. Etingof related to growth rates of tensor powers in symmetric tensor categories, we obtain general bounds on the order of finite subgroups of ${\rm GL}(n,\mathbb{C})$ with restricted composition…

We show that a group acting on a non-trivial tree with finite edge stabilizers and icc vertex stabilizers admits a faithful and highly transitive action on an infinite countable set. This result is actually true for infinite vertex…

In this short note we give a formula for the factorization number $F_2(G)$ of a finite rank $3$ abelian $p$-group $G$. This extends a result in our previous work \cite{9}.

We organize fundamental properties of quasi-Hamiltonian spaces on which a finite group acts, and we apply them to the theory of moduli spaces of flat connections on an oriented compact surface with boundary.

Let $G$ be a semisimple algebraic group whose decomposition into a product of simple components does not contain simple groups of type $A$, and $P\subseteq G$ be a parabolic subgroup. Extending the results of Popov [7], we enumerate all…

We show that every countable non-abelian free group $\Gamma $ admits a spherically transitive action on a rooted tree $T$ such that the action of $\Gamma $ on the boundary of $T$ is not essentially free. This reproves a result of Bergeron…