Related papers: $n$-transitivity of certain diffeomorphism groups

Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the Lie-Tresse theorem, but may change a lot. We describe in details the case of…

We consider a family of 2-step nilpotent Lie algebras associated to uniform complete graphs on odd number of vertices. We prove that the symmetry group of such a graph is the holomorph of the additive cyclic group $\Z_n$. Moreover, we prove…

For all Frobenius groups and a large class of finite multiply transitive permutation groups, we show that the corresponding group-subgroup subfactors are completely characterized by their principal graphs. The class includes all the sharply…

We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are…

We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.

We establish a sharp sufficient condition for groups acting on trees to be highly transitive when the action on the tree is minimal of general type. This gives new examples of highly transitive groups, including icc non-solvable…

We carry the argument used in the proof of the Theorem of Denjoy over to the quasiperiodically forced case. Thus we derive that if a system of quasiperiodically forced circle diffeomorphisms with bounded variation of the derivative has no…

A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…

Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.

We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs $ (G,\mathcal{M}) $, such that $ G $ is a finite 2-group and $ \mathcal{M}…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms $f$ on compact $3$-manifolds with fundamental groups of exponential growth such that $f^n$ is not homotopic to identity for all $n>0$.…

We introduce a new class of transitive permutation groups which properly contains the automorphism groups of vertex-transitive graphs and digraphs. We then give a sufficient condition for a quotient of this family to remain in the family,…

Suppose that a group $G$ has socle $L$ a simple large-rank classical group. Suppose furthermore that $G$ acts transitively on the set of lines of a linear space $\mathcal{S}$. We prove that, provided $L$ has dimension at least 25, then $G$…

We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational,…

We study nilpotent groups acting faithfully on complex algebraic varieties. We use a method of base change. For finite p-groups, we go from $k$, a number field, to a finite field in order to use counting lemmas. We show that a finite…

This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.

We prove that every countable acylindrically hyperbolic group admits a highly transitive action with finite kernel. This theorem uniformly generalizes many previously known results and allows us to answer a question of Garion and Glassner…

We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.

We study the action of the diffeomorphism group $\Diff(M)$ on the space of proper immersions $\Imm_{\text{prop}}(M,N)$ by composition from the right. We show that smooth transversal slices exist through each orbit, that the quotient space…