A criterion for the existence of normal \(\pi\) -complements in finite groups

DOI10.1016/0021-8693(84)90150-9zbMath0546.20017OpenAlexW1997631405MaRDI QIDQ798425

Zvi Arad, David Chillag

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0021-8693(84)90150-9

zbMATH Keywords

\(\pi\) -homogeneous\(\pi\) -subgroup\(\pi\) '-closedclassification of the finite simple groups

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Products of subgroups of abstract finite groups (20D40)

Related Items

On \(\pi\)-homogeneity and \(\pi\) '-closure, Classification of Finite Groups with a CC-Subgroup, Finite simple groups in which all maximal subgroups are \(\pi\)-closed. I., Determination of a finite group by certain subgroups and a solution to Szép's conjecture, Hereditary hyperradical formations, Any solubly saturated hereditary lattice formation is saturated., On the structure of \(\mathfrak {N}_{\sigma }\)-critical groups, The existence of normal π‐complements in finite groups, On formations of finite groups with the generalised Wielandt property for residuals., Finite groups with a system of generalized subnormal Schmidt subgroups, On the normalizers of \(\mathcal F\)-residuals of all subgroups of a finite group., On control of the prime spectrum of a finite simple group., Finite groups all of whose 2-maximal subgroups are \(\pi\)-decomposable., On one problem in formation theory.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Closure and dispersion of finite groups
• Direkte Produkte von Gruppen teilerfremder Ordnung
• Die Existenz Hallscher Normalteiler
• On a property like Sylow's of some finite groups
• Prime graph components of finite groups
• On 3-closure of 3'-homogeneous finite groups
• Semi-simple classes in Chevalley type groups
• Certain embeddings among finite groups of Lie type
• On a problem of Frobenius. II
• \(\pi\)-homogeneity and \(\pi '\)-closure of finite groups
• The classification of finite simple groups I. Simple groups and local analysis
• The non-abelian simple groups g, |g| < 10⁶— character tables
• ABSTRACT PROPERTIES OF THE SIMPLE SPORADIC GROUPS
• Involutions in Chevalley groups over fields of even order
• The 2-Transitive Permutation Representations of the Finite Chevalley Groups
• [https://portal.mardi4nfdi.de/wiki/Publication:4152718 On π � -Closure of π-Homogeneous Groups]
• Subgroups of Classical Groups Generated by Long Root Elements
• On Ree's Series of Simple Groups
• Endliche Gruppen I
• On a class of doubly transitive groups