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The uniqueness of groups of type J₄

Aschbacher, Michael and Segev, Yoav (1991) The uniqueness of groups of type J₄. Inventiones Mathematicae, 105 (1). pp. 589-607. ISSN 0020-9910. https://resolver.caltech.edu/CaltechAUTHORS:20200512-075747975

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Abstract

We give the first computer free proof of the uniqueness of groups of type J₄. In addition we supply simplified proofs of some properties of such groups, such as the structure of certain subgroups. A group of type J₄ is a finite group G possessing an involution z such that H=C_G(z) satisfies F*(H)=Q is extraspecial of order 2¹³, H/Q is isomorphic to Z₃ extended by Aut (M₂₂), and z^G ⋂ Q ≠ {z}. We prove: Main Theorem. Up to isomorphism there exists at most one group of type J₄.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/bf01232280DOIArticle
Additional Information:© 1991 Springer-Verlag. Oblatum VIII-1990 & 31-I-1991. This work was partially supported by BSF 88-00164. The first author is partially supported by NSF DMS-8721480 and NSA MDA 90-88-H-2032.
Funders:
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)88-00164
NSFDMS-8721480
National Security AgencyMDA 90-88-H-2032
Issue or Number:1
Record Number:CaltechAUTHORS:20200512-075747975
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200512-075747975
Official Citation:Aschbacher, M., Segev, Y. The uniqueness of groups of type J4. Invent Math 105, 589–607 (1991). https://doi.org/10.1007/BF01232280
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103122
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 May 2020 20:50
Last Modified:12 May 2020 20:50

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