Aschbacher, Michael and Guralnick, Robert and Segev, Yoav (2007) Elementary abelian 2-subgroups of Sidki-type in finite groups. Groups, Geometry, and Dynamics, 1 (4). pp. 347-400. ISSN 1661-7207. doi:10.4171/GGD/18. https://resolver.caltech.edu/CaltechAUTHORS:20100503-094555816
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Abstract
Let G be a finite group. We say that a nontrivial elementary abelian 2-subgroup V of G is of Sidki-type in G, if for each involution i in G, C_V(i) ≠ 1. A conjecture due to S. Sidki (J. Algebra 39, 1976) asserts that if V is of Sidki-type in G, then V ∩ 0_2(G) ≠ 1. In this paper we prove a stronger version of Sidki’s conjecture. As part of the proof, we also establish weak versions of the saturation results of G. Seitz (Invent. Math. 141, 2000) for involutions in finite groups of Lie type in characteristic 2. Seitz’s results apply to elements of order p in groups of Lie type in characteristic p, but only when p is a good prime, and 2 is usually not a good prime.
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| Additional Information: | © 2007 European Mathematical Society. Received November 3, 2006; revised March 6, 2007. Partially supported by NSF-0504852. Partially supported by NSF-0140578. Partially supported by BSF grant no. 2004-083. The referee report consisted of six pages of detailed, useful comments. We thank and applaud the referee for this work. | |||||||||
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| Subject Keywords: | finite simple groups; involutions; parabolic subgroups; fundamental subgroups; saturation | |||||||||
| Issue or Number: | 4 | |||||||||
| Classification Code: | Mathematics Subject Classification (2000): Primary 20D05; Secondary 20D06, 20D08. | |||||||||
| DOI: | 10.4171/GGD/18 | |||||||||
| Record Number: | CaltechAUTHORS:20100503-094555816 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100503-094555816 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 18097 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 05 May 2010 16:00 | |||||||||
| Last Modified: | 08 Nov 2021 23:41 |
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