### A proof of Ph. Hall's theorem on dimension subgroups

A. Grzegorek (1979)

Colloquium Mathematicae

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A. Grzegorek (1979)

Colloquium Mathematicae

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Changwen Li, Xuemei Zhang, Xiaolan Yi (2013)

Colloquium Mathematicae

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The major aim of the present paper is to strengthen a nice result of Shemetkov and Skiba which gives some conditions under which every non-Frattini G-chief factor of a normal subgroup E of a finite group G is cyclic. As applications, some recent known results are generalized and unified.

Jiří Parobek (1976)

Časopis pro pěstování matematiky

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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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Jasbir Singh Chahal (1979)

Mathematische Zeitschrift

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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.

L. M. Ezquerro, M. Gómez-Fernández, X. Soler-Escrivà (2005)

Bollettino dell'Unione Matematica Italiana

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In this paper we prove the following results. Let π be a set of prime numbers and G a finite π-soluble group. Consider U, V ≤ G and $H\in {\mathrm{Hall}}_{\pi}\left(G\right)$ such that $H\cap V\in {\mathrm{Hall}}_{\pi}\left(V\right)$ and $1\ne H\cap U\in {\mathrm{Hall}}_{\pi}\left(U\right)$. Suppose also $H\cap U$ is a Hall π-sub-group of some S-permutable subgroup of G. Then $H\cap U\cap V\in {\mathrm{Hall}}_{\pi}(U\cap V)$ and $\langle H\cap U,H\cap V\rangle \in {\mathrm{Hall}}_{\pi}\left(\langle U\cap V\rangle \right)$. Therefore,the set of all S-permutably embedded subgroups of a soluble group G into which a given Hall system Σ reduces is a sublattice of the lattice of all Σ-permutable subgroups of G. Moreover any two subgroups of this sublattice of coprimeorders...

Rolf Brandl, Libero Verardi (1992)

Rendiconti del Seminario Matematico della Università di Padova

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K. Szajowski (1976)

Applicationes Mathematicae

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Lavrov, K.G. (2005)

Zapiski Nauchnykh Seminarov POMI

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