Finite groups in \(\beta G\) (Q1308131)

The author gives a characterization of finite groups in the Stone-Čech compactification \(\beta G\) of a countable discrete group \(G\) and proves that if \(F\) is a finite subgroup with the identity \({\mathcal P}\) in \(\beta G\), then there exists a finite subgroup \(Y\) in \(G\) such that \(F=Y {\mathcal P}\) and \(y{\mathcal P}= {\mathcal P}y\) for each \(y\in Y\). Some applications of the above characterization are also presented.