Document Type: Research Paper
Department of Mathematics, Cork Institute of Technology, Bishopstown, Cork, Ireland.
Department of Computing and Mathematics, Waterford Institute of Technology, Waterford, Ireland
We determine the groups of minimal order in which all groups of order $n$ can embedded for $ 1 \le n \le 15$. We further determine the minimal order of a group in which all groups of order $n$ or less can be embedded, also for $ 1 \le n \le 15$.