1. Groups in which normality is a weakly transitive relation.
- Author
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Romano, Emanuela and Vincenzi, Giovanni
- Subjects
- *
GROUP theory , *GENERALIZATION , *MULTIPLY transitive groups , *FINITE groups , *MATHEMATICAL analysis - Abstract
We study groups in which normality is a weakly transitive relation, giving an extension of in Theorem A [On finite T-groups, J. Aust. Math. Soc. 75 (2003) 181-191] due to Ballester-Bolinches and Esteban-Romero pointing out the relations between these groups and those in which all subgroups are almost pronormal. Moreover, we extend a well-known theorem of Peng [Finite groups with pro-normal subgroups, Proc. Amer. Math. Soc. 20 (1969) 232-234] proving that for a large class of generalized FC-groups the weak transitivity of normality is equivalent to having finitely many maximal pronormalizers of subgroups. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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