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Published 2007 | public
Journal Article

Elementary abelian 2-subgroups of Sidki-type in finite groups

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.

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.

Additional details

Created:
August 22, 2023
Modified:
October 20, 2023