Minimal embeddings of small finite groups

Document Type: Research Paper


1 Department of Mathematics, Cork Institute of Technology, Bishopstown, Cork, Ireland.

2 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$‎.