0000000000813403
AUTHOR
D Otera
On Geometric Simple Connectivity
L'articolo intende dare una visione panoramica su ricerche recenti, molte delle quali sono da attribuire al V.Poenaru, sulla topologia di dimensione basse e sulla teoria geometrica dei gruppi.
On some recent investigations of probability in group theory
We describe some recent contributions on the probability of commuting pairs, introduced by P. Erdos, W. Gustafson and P. Turan around 1968 and 1973. Both combinatorial methods and character theory have significant application in this context and we illustrate some standard techniques and strategies, once generalizations of the probability of commuting pairs want to be studied. The importance of the subject is emphasized in some remarks and open questions, which reformulate some classical conjectures in group theory via a probabilistic approach.