A contribution to the theory of finite supersoluble groups
Luis M. Ezquerro (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Luis M. Ezquerro (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Mukherjee, N.P., Khazal, R. (1990)
International Journal of Mathematics and Mathematical Sciences
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Khazal, R., Mukherjee, N.P. (1989)
International Journal of Mathematics and Mathematical Sciences
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James C. Beidleman, Howard Smith (1993)
Publicacions Matemàtiques
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A θ-pair for a maximal subgroup M of a group G is a pair (A, B) of subgroups such that B is a maximal G-invariant subgroup of A with B but not A contained in M. θ-pairs are considered here in some groups having supersoluble maximal subgroups.
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.
Changwen Li (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Charles Holmes (1989)
Rendiconti del Seminario Matematico della Università di Padova
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Yangming Li (2010)
Rendiconti del Seminario Matematico della Università di Padova
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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 such that and . Suppose also is a Hall π-sub-group of some S-permutable subgroup of G. Then and . 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...