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.

Alghamdi, A., Otera, D., Russo, F. (2010). On some recent investigations of probability in group theory. BOLLETTINO DI MATEMATICA PURA E APPLICATA, 3, 87-96.

On some recent investigations of probability in group theory

RUSSO, Francesco
2010-01-01

Abstract

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.
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
Alghamdi, A., Otera, D., Russo, F. (2010). On some recent investigations of probability in group theory. BOLLETTINO DI MATEMATICA PURA E APPLICATA, 3, 87-96.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/55675
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