Title of article :
Probability of having nth-roots and n-centrality of two classes of groups
Author/Authors :
Hashemi, M. Faculty of Mathematical Sciences - University of Guilan, Rasht , Polkouei, M. Faculty of Mathematical Sciences - University of Guilan, Rasht
Abstract :
In this paper, we consider the nitely 2-generated groups K(s; l) and Gm as
follows;
K(s; l) = ⟨a; bjabs = bla; bas = alb⟩;
Gm = ⟨a; bjam = bm = 1; [a; b]a = [a; b]; [a; b]b = [a; b]⟩
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 :
Nilpotent groups , nth-roots , n-central groups
Journal title :
Astroparticle Physics
