Vincenzi, G. (2017). A characterization of soluble groups in which normality is a transitive relation. International Journal of Group Theory, 6(1), 21-27. doi: 10.22108/ijgt.2017.10890

Giovanni Vincenzi. "A characterization of soluble groups in which normality is a transitive relation". International Journal of Group Theory, 6, 1, 2017, 21-27. doi: 10.22108/ijgt.2017.10890

Vincenzi, G. (2017). 'A characterization of soluble groups in which normality is a transitive relation', International Journal of Group Theory, 6(1), pp. 21-27. doi: 10.22108/ijgt.2017.10890

Vincenzi, G. A characterization of soluble groups in which normality is a transitive relation. International Journal of Group Theory, 2017; 6(1): 21-27. doi: 10.22108/ijgt.2017.10890

A characterization of soluble groups in which normality is a transitive relation

A subgroup $X$ of a group $G$ is said to be an H-subgroup if N_{G}(X) ∩ X^{g }≤ X for each element $g$ belonging to $G$. In [M. Bianchi and e.a., On finite soluble groups in which normality is a transitive relation, J. Group Theory, 3 (2000) 147--156.] the authors showed that finite groups in which every subgroup has the H-property are exactly soluble groups in which normality is a transitive relation. Here we extend this characterization to groups without simple sections.

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