Hypercyclically embedded property and supersolvable fusion systems
Abstract
summary:Given a prime $p$ and a subgroup $A$ of a finite group $G$, we say that $A$ is a \hbox {$p$-${\rm CAP}$-subgroup} of $G$ if $A$ covers or avoids every $p$-$G$-chief factor, where a $p$-$G$-chief factor is a $G$-chief factor of order divisible by $p$. We say that $A$ is a strong $p$-${\rm CAP}$-subgroup of $G$ if $A$ is a $p$-${\rm CAP}$-subgroup of any subgroup of $G$ containing $A$. We use the concept of strong $p$-${\rm CAP}$-subgroups to investigate the $p\mathfrak {F}$-hypercentrally embedded property of normal subgroups of a finite group and obtain some new results. Moreover, we extend the concept of (strong) $p$-${\rm CAP}$-subgroups to fusion systems and use this to characterize supersolvable and nilpotent fusion systems.
Fields of Study & Subjects
Topological Materials and Phenomena
Physics of Superconductivity and Magnetism
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Czechoslovak Mathematical Journal
- Publisher
- Institute of Mathematics, Czech Academy of Sciences
- Volume
- 76
- Issue
- 2
- Pages
- 541–563
- Publication date
- 11 May 2026
- Language
- EN