On the probability distribution associated to commutator word map in finite groups \rom{2}
Abstract
Let $P(G)$ denotes the set of sizes of fibers of nontrivial commutators of the commutator word map. Here, we prove that $P(G)=1$, for any finite group $G$ of nilpotency class $3$ with exactlly two conjugacy class sizes. We also show that for given $n\geq 1$, there exists a finite group $G$ of nilpotency class $2$ with exactlly two conjugacy class sizes such that $P(G)=n$.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1805.00091
 Bibcode:
 2018arXiv180500091K
 Keywords:

 Mathematics  Group Theory;
 20D60;
 20P05
 EPrint:
 Minor correction in Lemma 2.6 and added one more lemma