On $\mathfrak{F}$-automizers of subgroups of finite groups

Abstract

Let $H$ be a subgroup of a group $G$ and $\mathfrak{F}$ a formation. Then the automizer of $H^{\mathfrak{F}}$ is called the $\mathfrak{F}$-automizer of $H$. In this paper, the properties of $\mathfrak{F}$-automizers of some soluble subgroups in a finite group are investigated.

Keywords

• finite group
• automorphism
• $\mathfrak{F}$-automizer
• $\mathfrak{F}$-residual

References

1. [1] R. Brandl, M. Deaconescu, Finite groups with small automizers of their nonabelian subgroups, Glasg. Math. J. 41, 59-64, 1999.