Karaduman, Erdal; Aydin, Hüseyin On the relationship between the recurrences in nilpotent groups and the binomial formula. (English) Zbl 1089.11011 Indian J. Pure Appl. Math. 35, No. 9, 1093-1103 (2004). If \(G\) is a nilpotent group of exponent \(p\) (\(p\) is a prime), nilpotency class \(n\) with a presentation \(G= \langle x_1,x_2,\dots, x_n,x_{n+1}| [x_2,x_1]=x_3, [x_3,x_1]=x_4,\dots,[x_n,x_1]=x_{n+1}\rangle \) then the authors examine the form of the entries of the two-step Fibonacci sequences formed by two elements of \(G\). Then they examine the relationship between the number of recurrence sums involved in the \(j\)th term of the last component of the Fibonacci sequences and the coefficient of the binomial formula \((a+b)^{n-2}, n \geq 2\). Reviewer: F. Pérez-Monasor (Valencia) Cited in 3 Documents MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11B65 Binomial coefficients; factorials; \(q\)-identities 20F18 Nilpotent groups Keywords:Fibonacci sequences; binomial formula; nilpotent groups PDFBibTeX XMLCite \textit{E. Karaduman} and \textit{H. Aydin}, Indian J. Pure Appl. Math. 35, No. 9, 1093--1103 (2004; Zbl 1089.11011)