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A characterization of soluble groups in which normality is a transitive relation | ||
| International Journal of Group Theory | ||
| مقاله 42، دوره 6، شماره 1، خرداد 2017، صفحه 21-27 اصل مقاله (193.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.10890 | ||
| نویسنده | ||
| Giovanni Vincenzi* | ||
| University of Salerno | ||
| چکیده | ||
| A subgroup $X$ of a group $G$ is said to be an H-subgroup if NG(X) ∩ Xg ≤ 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. | ||
| کلیدواژهها | ||
| $H$-subgroups؛ $T$-groups؛ pronormal subgroups؛ weakly normal subgroups؛ pronorm and H-norm of a group | ||
| مراجع | ||
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