a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...

The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. Th...

For a finitely generated group G = 〈A〉 where A = {a1, a2, . . . , an} the sequence xi = ai+1, 0 ≤ i ≤ n − 1, xi+n = ∏n j=1 xi+j−1, i ≥ 0, is called the Fibonacci orbit of G with respect to the generating set A, denoted FA(G). If FA(G) is periodic we call the length of the period of the sequence the Fibonacci length of G with respect to A, written LENA(G). In this paper we examine the Fibonacci ...

Data compression has been widely applied in many data processing areas. Compression methods use variable-length codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci code, as a representative of these codes, is often utilized for the compression of small numbers. Time consumption of encoding as well as decoding algorithms is importan...

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

For a finitely generated group G = 〈A〉 where A = {a1, a2, . . . , an} the sequence xi = ai+1, 0 ≤ i ≤ n − 1, xi+n = ∏n j=1 xi+j−1, i ≥ 0, is called the Fibonacci orbit of G with respect to the generating set A, denoted FA(G). If FA(G) is periodic, we call the length of the period of the sequence the Fibonacci length of G with respect to A, written LENA(G). We examine the Fibonacci lengths of al...

For a finitely generated group G = 〈A〉, where A = {a1, a2, . . . , an}, the sequence xi = ai, 1 ≤ i ≤ n, xi+n = ∏n j=1 xi+j−1, i ≥ 1, is called the Fibonacci orbit of G with respect to the generating set A, denoted FA(G). If FA(G) is periodic we call the length of the period of the sequence the Fibonacci length of G with respect to A, written LENA(G). In this paper we examine the Fibonacci leng...

Families of Fibonacci codes and Fibonacci representations are defined. Their main attributes are: (i) robustness, manifesting itself by the local containment of errors; (ii) simple encoding and and decoding. The main applica· tiOD explored is the transmission of binary strings whose length is in aD. unknown range, using robust Fibonacci representations instead of the conventional errorsensitive...