Aschbacher, Michael and Segev, Yoav (1991) The uniqueness of groups of type J₄. Inventiones Mathematicae, 105 (1). pp. 589-607. ISSN 0020-9910. doi:10.1007/bf01232280. 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 | ||||||||
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| 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. | ||||||||
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| Issue or Number: | 1 | ||||||||
| DOI: | 10.1007/bf01232280 | ||||||||
| 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: | 16 Nov 2021 18:18 |
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