Weakly normal subgroup

In mathematics, in the field of group theory, a subgroup $H$ of a group $G$ is said to be weakly normal if whenever $H^g\le N_G(H)$, we have $g\in N_G(H)$.

Every pronormal subgroup is weakly normal.

References

• Ballester-Bolinches, Adolfo; Esteban-Romero, R. (2003), "On finite T-groups", Journal of the Australian Mathematical Society 75 (2): 181–191, doi:10.1017/S1446788700003712, ISSN 1446-7887 
• Müller, Karl Hans (1966), "Schwachnormale Untergruppen: Eine gemeinsame Verallgemeinerung der normalen und normalisatorgleichen Untergruppen", Rendiconti del Seminario Matematico della Università di Padova. The Mathematical Journal of the University of Padova 36: 129–157, ISSN 0041-8994