On second minimal subgroups of Sylow subgroups of finite groups

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 2011 Spain English Publisher:Elsevier BVJournal:Journal of Algebra, volume 342, pages 134-146 (issn: 0021-8693,

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Authors: Ballester-Bolinches, Adolfo; Esteban Romero, Ramón; Li, Yangming;

doi: 10.1016/j.jalgebra.2011.06.016

handle: 10550/91042

On second minimal subgroups of Sylow subgroups of finite groups

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Abstract

A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids its chief factors. Partial cover and avoidance property has turned out to be very useful to clear up the group structure. In this paper, finite groups in which the second minimal subgroups of their Sylow p-subgroups, p a fixed prime, are partial CAP-subgroups are completely classified.

Country

Spain

Related Organizations

Universitat Politècnica de València
Spain
University of Valencia
Spain
Guangdong Institute of Education
China (People's Republic of)
University of Education, Winneba
Ghana

Keywords

Algebra and Number Theory, Supersoluble group, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, second minimal subgroups, Series and lattices of subgroups, finite groups, chief factors, Second minimal subgroup, chief series, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, partial CAP-subgroups, supersoluble groups, Àlgebra, Finite group, MATEMATICA APLICADA, Matemàtica, Partial CAP-subgroup, Partial cap-group

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