Search results for "probability of commuting pairs"
showing 2 items of 2 documents
On some recent investigations of probability in group theory
2010
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.
On the tensor degree of finite groups
2013
We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group.