nth-roots and n-centrality of finite ۲-generator p-groups of nilpotency class ۲

Here we consider all finite non-abelian ۲-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.

Keywords:

p-group , nth-roots , n-central group