Semidirect product of groups

In this BSc thesis we consider a construction of groups called semidirect product, which is a generalization of direct products. Semidirect products provide a much larger collection of groups than direct products. \n \nWe find a criterion, which enables us to determine whether a group is isomorphic to a semidirect product and discuss the difference between direct and semidirect products. We construct various examples of semidirect products and in particular semidirect products of cyclic groups. We exemplify that semidirect group products also take a role as symmetry groups of combinatorial objects such as graphs. \n