Chief factors, crowns, and the generalized Jordan-hölder theorem

DOI10.1080/00927879808823650zbMath0649.20020OpenAlexW2046582536MaRDI QIDQ3794387

Peter Förster

Publication date: 1988

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879808823650

zbMATH Keywords

crownscomplemented chief factorfinite soluble groupnon-Frattini chief factorgeneralized Jordan-Hölder Theorem

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Special subgroups (Frattini, Fitting, etc.) (20D25) Series and lattices of subgroups (20D30) Products of subgroups of abstract finite groups (20D40)

Related Items (14)

Complementation and chief factors III ⋮ A note on the Jordan-Hölder theorem ⋮ On boundedly generated subgroups of profinite groups. ⋮ The Jordan-Hölder theorem and prefrattini subgroups of finite groups ⋮ Crowns and factorization of the probabilistic zeta function of a finite group. ⋮ Prefrattini subgroups and crowns ⋮ An approach to outer fitting pairs defined by chief factors ⋮ GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS ⋮ Complementation and chief factors ik finite groups-II ⋮ Projective \(G\)-groups ⋮ Large characteristically simple sections of finite groups ⋮ On complemented nonabelian chief factors of a finite group ⋮ Complementation and chief factors in finite groups ⋮ On maximal subgroups of finite groups

Cites Work

• Projektive Klassen endlicher Gruppen. I: Schunck- und Gaschützklassen
• Maximal subgroups in composite finite groups
• Pre-Frattini groups.
• Nonabelian crowns and Schunck classes of finite groups
• Extreme classes of finite soluble groups
• Crowns and centralizers of chief factors of finite groups
• Eine note uber nichtabelsche hauptfaktoren und maximale untergruppen einer endlichen gruppe
• Closure operations for Schunck classes
• Homomorphs and formations of given derived class
• Varieties of groups

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