Masters Thesis

The power graphs of split metacyclic groups

We describe the power graphs of split metacylcic groups of order 2(2kp). We do this by looking at the order of the elements in the group and containment relationships among subgroups of maximal subgroups. Through finding the power graphs of this family of groups, we generalize results on the power graphs of dihedral and quasidihedral groups, and also contribute to the knowledge of explicit presentations of power graphs that are known, which is limited to mostly finite Abelian groups, and the aforemented D2n and Q4n.