All Questions

Let $G$ be a finite non-abelian group of $n$ elements. I would like a measure that intuitively captures the extent to which $G$ is non-commutative. One easy measure is a count of the non-commutative ...

In wonderful lectures by P. Diaconis "Group representations in probability and statistics, Chapter 6. Metrics on Groups, and Their Statistical Use" metrics on permutation groups are considered and ...

This question asks for intuition, not a proof. An earlier question, Measures of non-abelian-ness was thoroughly answered by Arturo Magidin. A paper by Gustafson1 proves that, for a nonabelian group, ...

Standard setup. Consider a group and choose generators. Word-metric (or in the other words - distance on the Cayley graph of the group+generators) - converts a group into a metric space, which is ...

It is not uncommon to read that "nilpotent groups are 'close to abelian'."1,2 Can this sentiment be made precise in the sense of the Turán and Erdős definition of "the probability that two elements of ...