Probability of having $n^{th}$-roots and n-centrality of two classes of groups

Authors

  • M. Hashemi Faculty of Mathematical Sciences, University of Guilan, P.O.Box 41335-19141, Rasht, Iran
  • M. Polkouei 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:$$K(s,l)=langle a,b|ab^s=b^la, ba^s=a^lbrangle,\G_m=langle a,b|a^m=b^m=1, {[a,b]}^a=[a,b], {[a,b]}^b=[a,b]rangle$$ 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.

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Journal title

volume 05  issue 01

pages  55- 62

publication date 2016-06-01

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