On combinatorial and affine automorphisms of polytopes

We disprove the longstanding conjecture that every combinatorial automorphism of the boundary complex of a convex polytope in euclidean spaceE ^d can be realised by an affine transformation ofE ^d .     

Groups of automorphisms and PI-algebras

Siberian Mathematical Journal -     

Dense orbits of automorphisms and compactness of groups

It is proved, by using topological properties, that when a group automorphism of a locally compact totally disconnected group is ergodic under the Haar measure, the group is compact. The result is an answer for Halmos's question that has remained open for the totally disconnected case.     

Groups of automorphisms of finite p-groups

Thompson [1] showed that if p is an odd prime number, A is a p-group of operators of the finite group P in which the Frattini subgroup (P) is elementary and central, and P/(P) is a free Z_pA-module, then Cp(A) covers C_P/(P)(A). Then he proposed the question of whether it is possible in this theorem to weaken the hypothesis that (P) be elementary and central. In the work it is shown that this hypothesis may be replaced by a much weaker one; it is sufficient that P be met-Abelian and have nilpotence class 相似文献   

Groups with regular automorphisms of order four

Mathematische Zeitschrift -     

On automorphisms of n-dimensional Laguerre space

We examine some properties of two types of inversions in the isotropical model of n-dimensional Laguerre space. Moreover we establish an isomorphism between the isotropical and the cylinder models of the n-dimensional Laguerre space. We prove also that every automorphism of the n-dimensional Laguerre space is a composition of a pseudodilatation and some involutive maps.     

Groups of automorphisms of finite regular cubic graphs

Dedicated to the memory of A. I. Mal'tsev.