Probability of having $n^{th}$-roots and n-centrality of two classes of groups
الموضوعات :
1 - Faculty of Mathematical Sciences, University of Guilan, P.O.Box 41335-19141, Rasht, Iran
2 - Faculty of Mathematical Sciences, University of Guilan, P.O.Box 41335-19141, Rasht, Iran
الکلمات المفتاحية: Nilpotent groups, n-central groups, $n^{th}$-roots,
ملخص المقالة :
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, weinvestigate integers n for which, these groups are n-central.
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