A condition for the solvability of finite groups.
Miao, Long, Qian, Guohua (2009)
Sibirskij Matematicheskij Zhurnal
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Miao, Long, Qian, Guohua (2009)
Sibirskij Matematicheskij Zhurnal
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Kondrat'ev, A.S., Guo, Wenbin (2009)
Sibirskij Matematicheskij Zhurnal
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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.
Erfanian, Ahmad, Russo, Francesco (2009)
Acta Universitatis Apulensis. Mathematics - Informatics
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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.
Noskov, Guennadi A., Vinberg, Èrnest B. (2002)
Journal of Lie Theory
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Chigira, Naoki, Iiyori, Nobuo, Yamaki, Hiroyoshi (1998)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Fausto De Mari, Francesco de Giovanni (2005)
Colloquium Mathematicae
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The structure of (generalized) soluble groups for which the set of all subnormal non-normal subgroups satisfies the maximal condition is described, taking as a model the known theory of groups in which normality is a transitive relation.
Erfanian, Ahmad, Russo, Francesco G. (2010)
Acta Universitatis Apulensis. Mathematics - Informatics
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I.M.S. Dey, J. Cossey, S. Meskin (1971)
Mathematische Zeitschrift
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Lempken, Wolfgang, van Trung, Tran (2005)
Experimental Mathematics
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Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramón Esteban-Romero (2013)
Open Mathematics
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In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
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.
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.