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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.
A. Ballester-Bolinches, M. D. Pérez-Ramos (1995)
Rendiconti del Seminario Matematico della Università di Padova
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Yong Xu, Xianhua Li (2016)
Open Mathematics
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We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.
Jindřich Bečvář (1977)
Commentationes Mathematicae Universitatis Carolinae
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Luis M. Ezquerro (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Adolfo Ballester-Bolinches, James Beidleman, Ramón Esteban-Romero, Vicent Pérez-Calabuig (2013)
Open Mathematics
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A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable...