An f-essential subgroup is called a pearl if it is either elementary abelian of order p2 or non-abelian of order p3. In this paper we start the investigation of fusion systems containing pearls: we determine a bound for the order of p-groups containing pearls and we classify the saturated fusion systems on p-groups containing pearls and having sectional rank at most 4.
- Fusion systems
- Elementary abelian essential subgroup
- Extraspecial essential subgroup
- p-Groups of maximal nilpotency class
- --Groups of sectional rank at most 4