Document Type: Research Paper

**Authors**

Faculty of Mathematical Sciences, University of Guilan, P.O.Box 41335-19141, Rasht, Iran

**Abstract**

In this paper, we consider the finitely 2-generated groups $K(s,l)$ and $G_m$ as follows:

$$K(s,l)=\langle a,b|ab^s=b^la, ba^s=a^lb\rangle,\\

G_m=\langle a,b|a^m=b^m=1, {[a,b]}^a=[a,b], {[a,b]}^b=[a,b]\rangle$$

and find the explicit formulas for the probability of having nth-roots for them. Also, we investigate integers n for which, these groups are n-central.

**Keywords**

**Main Subjects**

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