James Beidleman, Hermann Heineken (2003)
Bollettino dell'Unione Matematica Italiana
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We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow -subgroups for permute with all subnormal subgroups.
Luis M. Ezquerro (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Wenai Yan, Baojun Li, Zhirang Zhang (2013)
Colloquium Mathematicae
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Let ℨ be a complete set of Sylow subgroups of a group G. A subgroup H of G is called ℨ-permutably embedded in G if every Sylow subgroup of H is also a Sylow subgroup of some ℨ-permutable subgroup of G. By using this concept, we obtain some new criteria of p-supersolubility and p-nilpotency of a finite group.
A. Ballester-Bolinches, M. D. Pérez-Ramos (1995)
Rendiconti del Seminario Matematico della Università di Padova
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Leonid A. Kurdachenko, Igor Ya. Subbotin (2007)
Commentationes Mathematicae Universitatis Carolinae
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The article is dedicated to groups in which the set of abnormal and normal subgroups (-subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.
Leonid Kurdachenko, Alexsandr Pypka, Igor Subbotin (2010)
Open Mathematics
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New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.
de Falco, M., de Giovanni, F. (2001)
Serdica Mathematical Journal
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A subgroup H of a group G is said to be quasinormal if HX = XH for all subgroups X of G. In this article groups are characterized for which the partially ordered set of quasinormal subgroups is decomposable.