Weakly normal subgroup

In mathematics, in the field of group theory, a subgroup [math]\displaystyle{ H }[/math] of a group [math]\displaystyle{ G }[/math] is said to be weakly normal if whenever [math]\displaystyle{ H^g \leq N_G(H) }[/math], we have [math]\displaystyle{ g \in N_G(H) }[/math].

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