The classification of finite simple groups I. Simple groups and local analysis

DOI10.1090/S0273-0979-1979-14551-8zbMath0414.20009OpenAlexW2037832379WikidataQ55890187 ScholiaQ55890187MaRDI QIDQ3048992

Daniel Gorenstein

Publication date: 1979

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1979-14551-8

zbMATH Keywords

sporadic simple groupsfinite simple groupsBibliographyfactorizationslocal analysisfinite Chevalley groupsMonster groupK-grouppushing up theoremssignalizer functorsJanko groupSteinberg relations(B,N)-pairLeech lattices3- transpositionscentralizer of involution characterizationsconnected simple groups of component typek-balanced groupsknown finite simple groupsnonconnected simple groupsodd local rankrank 3-permutation groupsrecognition theoremssimple groups of characteristic 2-typestrongly embedding theorem

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Finite simple groups and their classification (20D05) Simple groups: alternating groups and groups of Lie type (20D06) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (26)

The string C-group representations of the Suzuki, Rudvalis and O'Nan sporadic groups ⋮ Classifying the finite simple groups ⋮ On the ranks of \(O'N\) and \(Ly\). ⋮ Non-deductive Logic in Mathematics: The Probability of Conjectures ⋮ Classification of finite groups by a maximal subgroup ⋮ Finite groups with given centralizer of a central involution ⋮ Prime graph components of finite groups ⋮ Finite groups which possess a strongly closed 2-subgroup of class at most two. I, II ⋮ Finite simple groups with 3-constrained 3-local subgroups ⋮ Standard subgroups isomorphic to \(^2 F_4(2^n)\) ⋮ A brief history of the classification of the finite simple groups ⋮ A coprime action version of a solubility criterion of Deskins ⋮ Finite groups ⋮ The classification of the finite simple groups ⋮ A class of finite groups with abelian centralizer of an element of order 3 of type \((3,2,2)\). ⋮ Correction to: ``A coprime action version of a solubility criterion of Deskins ⋮ S-rings over loops, right mapping groups and transversals in permutation groups ⋮ On a geometry of Ivanov and Shpectorov for the O'Nan sporadic simple group ⋮ Certain 2-local blocks with alternating sections ⋮ Extreme pairs for finite groups ⋮ The Coxeter–Todd lattice, the Mitchell group, and related sphere packings ⋮ Simple locally finite groups with the minimal condition for 2-subgroups ⋮ On the product of two finite groups with centers of even order ⋮ The efficiency of simple groups of order < 10⁵ ⋮ Classification of periodic linear groups over fields of odd characteristic ⋮ A criterion for the existence of normal \(\pi\) -complements in finite groups

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