1California Institute of Technology, Pasadena, USA 2University of Southern California, Los Angeles, United States 3Ben-Gurion University, Beer-Sheva, Israel
Groups, geometry, and dynamics, Tome 1 (2007) no. 4, pp. 347-400
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, CV(i) = 1. A conjecture due to S. Sidki (J. Algebra 39, 1976) asserts that if V is of Sidki-type in G, then V ∩ O2(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.
Michael Aschbacher
1
;
Robert M. Guralnick
2
;
Yoav Segev
3
1
California Institute of Technology, Pasadena, USA
2
University of Southern California, Los Angeles, United States
3
Ben-Gurion University, Beer-Sheva, Israel
Michael Aschbacher; Robert M. Guralnick; Yoav Segev. Elementary abelian 2-subgroups of Sidki-type in finite groups. Groups, geometry, and dynamics, Tome 1 (2007) no. 4, pp. 347-400. doi: 10.4171/ggd/18
@article{10_4171_ggd_18,
author = {Michael Aschbacher and Robert M. Guralnick and Yoav Segev},
title = {Elementary abelian 2-subgroups of {Sidki-type} in finite groups},
journal = {Groups, geometry, and dynamics},
pages = {347--400},
year = {2007},
volume = {1},
number = {4},
doi = {10.4171/ggd/18},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/18/}
}
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