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.
A CHARACTERIZATION OF SOLUBLE GROUPS IN WHICH NORMALITY IS A TRANSITIVE RELATION
VINCENZI, Giovanni
2017
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.File in questo prodotto:
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