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EnglishA 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 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.
| Titolo: | A CHARACTERIZATION OF SOLUBLE GROUPS IN WHICH NORMALITY IS A TRANSITIVE RELATION |
| Autori: | |
| Data di pubblicazione: | 2017 |
| Rivista: | |
| Abstract: | 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 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. |
| Handle: | http://hdl.handle.net/11386/4650033 |
| Appare nelle tipologie: | 1.1.2 Articolo su rivista con ISSN |
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