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In [[mathematics]], in the field of [[group theory]], a [[subgroup]] <math>H</math> of a [[group (mathematics)|group]] <math>G</math> is said to be '''weakly normal''' if whenever <math>H^g \leq N_G(H)</math>, we have <math>g \in N_G(H)</math>.  
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Every [[pronormal subgroup]] is weakly normal.
 
==References==
* {{Citation | doi=10.1017/S1446788700003712 | last1=Ballester-Bolinches | first1=Adolfo | last2=Esteban-Romero | first2=R. | title=On finite T-groups | id={{MathSciNet | id = 2000428}} | year=2003 | journal=Journal of the Australian Mathematical Society | issn=1446-7887 | volume=75 | issue=2 | pages=181–191}}
* {{Citation | last1=Müller | first1=Karl Hans | title=Schwachnormale Untergruppen: Eine gemeinsame Verallgemeinerung der normalen und normalisatorgleichen Untergruppen | id={{MathSciNet | id = 0204528}} | year=1966 | journal=Rendiconti del Seminario Matematico della Università di Padova. the Mathematical Journal of the University of Padova | issn=0041-8994 | volume=36 | pages=129–157}}
 
[[Category:Group theory]]
[[Category:Subgroup properties]]
 
 
{{Abstract-algebra-stub}}

Latest revision as of 12:05, 8 December 2014

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