on the t-nacci sequences of some finite groups of nilpotency class two

We consider nite groups hm and gmn as follows:hm =.x; yjxm2= ym = 1; y..1xy = x1+m.; m  2;gmn =.x; yjxm = yn = 1; [x; y]x = [x; y]; [x; y]y = [x; y]. m; n  2:in this paper, we rst study the groups hm and gmn. then by using theproperties of hm, gmm and t..nacci sequences in nite groups, we show thatthe period of t..nacci sequences in these groups are a multiple of wall numberk(t;m).