On the solvability of regular subgroups in the holomorph of a finite solvable group

DOI10.1142/S0218196719500735zbMath1493.20002arXiv1901.10636WikidataQ114614812 ScholiaQ114614812MaRDI QIDQ5221278

Cindy (Sin Yi) Tsang, Chao Qin

Publication date: 25 March 2020

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.10636

zbMATH Keywords

regular subgroupholomorphHopf-Galois structurefinite solvable groupskew brace

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Separable extensions, Galois theory (12F10) Subgroups of symmetric groups (20B35) General theory for finite permutation groups (20B05) Hopf algebras and their applications (16T05)

Related Items (11)

Hopf-Galois structures on cyclic extensions and skew braces with cyclic multiplicative group ⋮ Hopf-Galois structures on extensions of degree \(p^2q\) and skew braces of order \(p^2q\): the cyclic Sylow \(p\)-subgroup case ⋮ Hopf-Galois structures on finite extensions with almost simple Galois group ⋮ Module braces: relations between the additive and the multiplicative groups ⋮ Non‐abelian simple groups which occur as the type of a Hopf–Galois structure on a solvable extension ⋮ On insoluble transitive subgroups in the holomorph of a finite soluble group ⋮ Mini-workshop: Skew braces and the Yang-Baxter equation. Abstracts from the mini-workshop held February 26 -- March 4, 2023 ⋮ Finite skew braces with solvable additive group ⋮ Rota-Baxter groups, skew left braces, and the Yang-Baxter equation ⋮ Hopf–Galois structures on finite extensions with quasisimple Galois group ⋮ Hopf-Galois realizability of \(\mathbb{Z}_n \rtimes \mathbb{Z}_2\)

Uses Software

• GAP
• Magma
• OEIS
• Cubefree

Cites Work

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• Produkte nilpotenter Gruppen
• Solubility criteria for Hopf-Galois structures
• The Magma algebra system. I: The user language
• Non-existence of Hopf-Galois structures and bijective crossed homomorphisms
• Addendum to ``On the groups of cube-free order.
• On skew braces (with an appendix by N. Byott and L. Vendramin)
• Hopf-Galois structures on a Galois \(S_n\)-extension
• On finite simple groups of order divisible by three primes only
• Simple groups of order \(7 \cdot 3^a \cdot 2^b\)
• Über das Produkt von zwei abelschen Gruppen
• Skew braces and the Yang–Baxter equation
• A NEW TYPE OF SIMPLE GROUPS OF FINITE ORDER
• ON THE SUPERSOLVABILITY OF BICYCLIC GROUPS
• The Finite Simple Groups
• HOPF–GALOIS STRUCTURES ON FIELD EXTENSIONS WITH SIMPLE GALOIS GROUPS
• A MILLENNIUM PROJECT: CONSTRUCTING SMALL GROUPS
• On simple groups of order 5⋅3^{𝑎}⋅2^{𝑏}
• A search for Wieferich and Wilson primes

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