Some Observations Regarding the Holomorphs of Finite Abelian Groups

Abstract

Presentations for the holomorphs of abelian groups of the form $C_{p^n}\times 1^m$ for $p$=2 or an odd prime are given. These presentations extend the results given in Burnside's well-known text on finite groups on the holomorphs for the cyclic groups of orders $p^n$ for $p$ being an odd or even prime.