On complemented nonabelian chief factors of a finite group

DOI10.1007/BF02773467zbMath0915.20014OpenAlexW2073184624MaRDI QIDQ1269768

Paz Jiménez-Seral, Julio P. Lafuente

Publication date: 7 July 1999

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02773467

zbMATH Keywords

maximal subgroupsnormal subgroupscomplementspairingschief seriesJordan-Hölder theoremcomplemented Abelian chief factorsnumbers of complemented chief factors

Mathematics Subject Classification ID

General structure theorems for groups (20E34) Chains and lattices of subgroups, subnormal subgroups (20E15) Derived series, central series, and generalizations for groups (20F14) Symmetric groups (20B30)

Related Items (19)

Genus, thickness and crossing number of graphs encoding the generating properties of finite groups ⋮ A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group ⋮ FINITE GROUPS WITH INDEPENDENT GENERATING SETS OF ONLY TWO SIZES ⋮ Crowns and factorization of the probabilistic zeta function of a finite group. ⋮ Prefrattini subgroups and crowns ⋮ The minimum generating set problem ⋮ Finite groups, minimal bases and the intersection number ⋮ A decomposition theorem for group representations. ⋮ GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS ⋮ Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function. ⋮ The Chebotarev invariant of a finite group: A conjecture of Kowalski and Zywina ⋮ Projective \(G\)-groups ⋮ Finite groups with large Chebotarev invariant ⋮ Minimal invariable generating sets ⋮ On complemented non-abelian chief factors of a Lie algebra ⋮ Characterization of finitely generated infinitely iterated wreath products ⋮ Clifford theory for semisimple \(G\)-groups ⋮ Bounds on the number of maximal subgroups of finite groups ⋮ An upper bound on the Chebotarev invariant of a finite group

Cites Work

• Some applications of the first cohomology group
• On normal subgroups which are direct products
• Pre-Frattini groups.
• On the second Loewy term of projectives of a group algebra
• Nonabelian crowns and Schunck classes of finite groups
• Cohomologie galoisienne. Cours au Collège de France, 1962--1963. Seconde édition.
• Cohomological topics in group theory.
• Chief factors, crowns, and the generalized Jordan-hölder theorem
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