Hashemi, M., Polkouei, M. (2016). Probability of having $n^{th}$-roots and n-centrality of two classes of groups. Journal of Linear and Topological Algebra (JLTA), 05(01), 55-62.

M. Hashemi; M. Polkouei. "Probability of having $n^{th}$-roots and n-centrality of two classes of groups". Journal of Linear and Topological Algebra (JLTA), 05, 01, 2016, 55-62.

Hashemi, M., Polkouei, M. (2016). 'Probability of having $n^{th}$-roots and n-centrality of two classes of groups', Journal of Linear and Topological Algebra (JLTA), 05(01), pp. 55-62.

Hashemi, M., Polkouei, M. Probability of having $n^{th}$-roots and n-centrality of two classes of groups. Journal of Linear and Topological Algebra (JLTA), 2016; 05(01): 55-62.

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

^{}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.

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