On the Basic k-nacci Sequences in Finite Groups

K-nacci Sequences in Finite Triangle Groups

A k-nacci sequence in a finite group is a sequence of group elements x0, x1, x2, . . . , xn, . . . for which, given an initial seed set x0, x1, x2, . . . , xj−1 , each element is defined by xn x0x1 . . . xn−1, for j ≤ n < k, and xn xn−kxn−k 1 . . . xn−1, for n ≥ k. We also require that the initial elements of the sequence, x0, x1, x2, . . . , xj−1, generate the group, thus forcing the k-nacci s...

The k-nacci Sequences and The Generalized Order-k Pell Sequences in The Semi-Direct Product of Finite Cyclic Groups

The Jacobsthal Sequences in Finite Groups

Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...

Non-Abelian Sequenceable Groups Involving ?-Covers

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...

On the Regular Power Graph on the Conjugacy Classes of Finite Groups

emph{The (undirected) power graph on the conjugacy classes} $mathcal{P_C}(G)$ of a group $G$ is a simple graph in which the vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent in $mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.