‎this article presents a systematic study for structure of finite wavelet frames‎ ‎over prime fields‎. ‎let $p$ be a positive prime integer and $mathbb{w}_p$‎ ‎be the finite wavelet group over the prime field $mathbb{z}_p$‎. ‎we study theoretical frame aspects of finite wavelet systems generated by‎ ‎subgroups of the finite wavelet group $mathbb{w}_p$.

‎let $g$ be a group and $a=aut(g)$ be the group of automorphisms of‎ ‎$g$‎. ‎then the element $[g,alpha]=g^{-1}alpha(g)$ is an‎ ‎autocommutator of $gin g$ and $alphain a$‎. ‎also‎, ‎the‎ autocommutator subgroup of g is defined to be‎ ‎$k(g)=langle[g,alpha]|gin g‎, ‎alphain arangle$‎, ‎which is a‎ ‎characteristic subgroup of $g$ containing the derived subgroup‎ ‎$g'$ of $g$‎. ‎a group is defined...

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 ...