### SE-supplemented subgroups of finite groups

Wenbin Guo, Alexander N. Skiba, Nanying Yang (2013)

Rendiconti del Seminario Matematico della Università di Padova

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Wenbin Guo, Alexander N. Skiba, Nanying Yang (2013)

Rendiconti del Seminario Matematico della Università di Padova

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Xianhua Li, A. Ballester-Bolinches (2006)

Bollettino dell'Unione Matematica Italiana

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In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.

Kazakevich, V.G., Stavrova, A.K. (2004)

Zapiski Nauchnykh Seminarov POMI

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Al-Sharo, K. (2008)

Beiträge zur Algebra und Geometrie

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A. Grzegorek (1979)

Colloquium Mathematicae

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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 $p$-subgroups for $p<7$ permute with all subnormal subgroups.

Rolf Brandl, Libero Verardi (1992)

Rendiconti del Seminario Matematico della Università di Padova

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Huaguo Shi, Zhangjia Han (2012)

Colloquium Mathematicae

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We describe finite groups which contain just one conjugate class of self-normalizing subgroups.

Kurdachenko, L. A., Subbotin, I. Ya. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 20F16, 20E15. Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.

Jiří Parobek (1976)

Časopis pro pěstování matematiky

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John G. Thompson, Zvonimir Janko (1970)

Mathematische Zeitschrift

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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.