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The existence of J₃ and its embeddings in E₆

Aschbacher, Michael (1990) The existence of J₃ and its embeddings in E₆. Geometriae Dedicata, 35 (1-3). pp. 143-154. ISSN 0046-5755. doi:10.1007/bf00147344.

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We determine the embeddings of the third sporadic group J₃ of Janko in simple Chevalley groups of type E₆ over finite and algebraically closed fields. As a corollary we obtain a short elegant existence proof of J₃. This is of interest as J₃ is one of the few sporadic groups not contained in the Monster, so its existence cannot be verified within that group. Previous existence proofs were highly computational; cf. [4] and [6].

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Additional Information:© 1990 Kluwer Academic Publishers. Received 25 August 1989; Issue Date September 1990. To Jacques Tits on his sixtieth birthday. Partially supported by NSF DMS-8721480 and NSA MDA90-88-H-2032.
Funding AgencyGrant Number
National Security AgencyMDA 90-88-H-2032
Subject Keywords:Chevalley Group; Existence Proof; Sporadic Group; Previous Existence; Simple Chevalley Group
Issue or Number:1-3
Record Number:CaltechAUTHORS:20200512-071755284
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Official Citation:Aschbacher, M. The existence of J3 and its embeddings in E6. Geom Dedicata 35, 143–154 (1990).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103116
Deposited By: Tony Diaz
Deposited On:12 May 2020 20:23
Last Modified:16 Nov 2021 18:18

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