Strong restrictions on the structure of a group $G$ can be given, once that it is known the probability that a randomly chosen pair of elements of a finite group $G$ commutes. Introducing the notion of mutually commuting n-tuples for compact groups (not necessary finite), the present paper generalizes the probability that a randomly chosen pair of elements of $G$ commutes. We shall state some results concerning this new concept of probability which has been recently treated in [3]. Furthermore a relation has been found between the notion of mutually commuting n-tuples and that of isoclinism between two arbitrary groups.

Erfanian, A., Russo, F. (2009). Isoclinism in probability of commuting n-tuples. ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 25, 27-36.

Isoclinism in probability of commuting n-tuples

RUSSO, Francesco
2009-01-01

Abstract

Strong restrictions on the structure of a group $G$ can be given, once that it is known the probability that a randomly chosen pair of elements of a finite group $G$ commutes. Introducing the notion of mutually commuting n-tuples for compact groups (not necessary finite), the present paper generalizes the probability that a randomly chosen pair of elements of $G$ commutes. We shall state some results concerning this new concept of probability which has been recently treated in [3]. Furthermore a relation has been found between the notion of mutually commuting n-tuples and that of isoclinism between two arbitrary groups.
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
Erfanian, A., Russo, F. (2009). Isoclinism in probability of commuting n-tuples. ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 25, 27-36.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/55673
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