Theorems on Simple Groups

Ergodic Theorems on Amenable Groups

Ergodic Theorems on Amenable Groups

In 1931, Birkhoff gave a general and rigorous description of the ergodic hypothesis from statistical meachanics. This concept can be generalized by group actions of a large class of amenable groups on σ-finite measure spaces. The expansion of this theory culminated in Lindenstrauss’ celebrated proof of the general pointwise ergodic theorem in 2001. The talk is devoted to the introduction of abs...

Two Theorems on Doubly Transitive Permutation Groups

In a series of papers [3, 4 and 5] on insoluble (transitive) permutation groups of degree p = 2q +1, where p and q are primes, N. Ito has shown that, apart from a small number of exceptions, such a group must be at least quadruply transitive. One of the results which he uses is that an insoluble group of degree p = 2q +1 which is not doubly primitive must be isomorphic to PSL (3, 2) with p = 7....

Lindeberg–Feller theorems on Lie groups

`=1 ∫ |x|>ε |x| μn`(dx) = 0 for all ε > 0, where x 7→ |x| denotes a fixed homogeneous norm on the Heisenberg group. Professor E. Siebert suggested a way to prove similar results for a Lie group G. The main step is the generalization of Lemma 1 in Pap [4] for an arbitrary Lie group G, which gives an estimation for the Fourier transform of a probability measure on G in terms of integrals of local...

Intersection theorems in permutation groups

The Hamming distance between two permutations of a finite set X is the number of elements of X on which they differ. In the first part of this paper, we consider bounds for the cardinality of a subset (or subgroup) of a permutation group P on X with prescribed distances between its elements. In the second part. We consider similar results for sets of s-tuples of permutations; the role of Hammin...