TY - JOUR

T1 - Elementary abelian 2-subgroups of Sidki-type in finite groups

AU - Aschbacher, Michael

AU - Guralnick, Robert

AU - Segev, Yoav

PY - 2007/1/1

Y1 - 2007/1/1

N2 - 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

AB - 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

U2 - 10.4171/GGD/18

DO - 10.4171/GGD/18

M3 - מאמר

SN - 1661-7207

VL - 1

SP - 347

EP - 400

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 4

ER -