2019
Том 71
№ 1

Fibonacci lengths of all finite $p$-groups of exponent $p^2$

Abstract

The Fibonacci lengths of finite p-groups were studied by Dikici and coauthors since 1992. All considered groups are of exponent $p$ and the lengths depend on the Wall number $k(p)$. The p-groups of nilpotency class 3 and exponent $p$ were studied in 2004 also by Dikici. In the paper, we study all $p$-groups of nilpotency class 3 and exponent $p^2$. Thus, we complete the study of Fibonacci lengths of all $p$-groups of order $p^4$ by proving that the Fibonacci length is $k(p^2)$.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 5, pp 665-673.

Citation Example: Ahmadi B., Doostie H. Fibonacci lengths of all finite $p$-groups of exponent $p^2$ // Ukr. Mat. Zh. - 2013. - 65, № 5. - pp. 603–610.