University of GuilanJournal of Algebra and Related Topics2345-39313220151201nth-roots and n-centrality of finite 2-generator p-groups of nilpotency class 261711542ENM. PolkoueiUniversity of GuilanM. HashemiUniversity of GuilanJournal Article20151201Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.https://jart.guilan.ac.ir/article_1542_21a4c2d0eea4260bab01d638f0dd1e22.pdf