let h be a subgroup of a group g. h is said to be s-embedded in g if g has a normal t such that ht is an s-permutable subgroup of g and h ∩ t ≤ h sg, where h denotes the subgroup generated by all those subgroups of h which are s-permutable in g. in this paper, we investigate the influence of minimal s-embedded subgroups on the structure of finite groups. we determine the structure the finite grou...

‎in the following text for arbitrary $x$ with at least two elements‎, ‎nonempty countable set $gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map‎. ‎we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney‎, ‎exact dev...