\titleofpresentation{On the Probability Mutually Commuting $n$-tuples
  in Compact Groups} 
\presenter{A. Erfanian}

Let
$\mathrm{Pr}_n\mathrm{Com}(G)$ denotes the probability that a randomly ordered
$n$-tuples of elements in a finite group $G$ be a mutually
commuting $n$-tuples. We aim to generalize the above concept to a
compact topological group which generally not only finite but also
even uncountable. The results are mostly new or improvements of
known
results in finite case given in \cite{erfanian1,erfanian2,erfanian3}. 


\begin{ourbiblio}{9}
\bibitem{erfanian1} Erdös, P. and Turan, P., On some problems of statistical group theory, {\it Acta Math.
 Acad. Sci. Hung.} 19 (1968),413-435.
1031-1304.
\bibitem{erfanian2} Gallagher, P. X., The number of Conjugacy classes in
a finite group, {\it Math. Z.} 118 (1970), 175-179.
\bibitem{erfanian3} Gustafon, W. H., What is the probability that two groups
elements commute? , {\it Amer. Math. Monthly} 80 (1973),
1031-1304.
\end{ourbiblio}

\presenteraddress{Department of Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran}

\email{erfanian@math.um.ac.ir}

