  We prove additive and multiplicative partition theorems, obtaining
combinatorial results for p-quasicyclic groups, where p is a prime number. We
also get density results for p-quasicyclic groups via left F{\o}lner sequences
of non-empty finite subsets of it, giving a sufficient condition in order a
subset of a p-quasicyclic group to contain arbitrary long arithmetic
progressions. Finally, we introduce the notion of a dynamical system over
p-quasicyclic groups extending the classical notion of a topological dynamical
system and we prove (multiple) recurrent results for the p-quasicyclic groups.
In particular, we prove recurrent results analogous to Furstenberg-Weiss type
theorems for classical systems.
