Abstract
In [6], J. Tits has shown that the Ree group 2F4(2) is not simple but possesses a
simple subgroup of index 2.
In this paper we prove the following theorem:THEOREM. Let G be a finite group of even order and let z be an
involution contained in G. Suppose H = CG(z) has the following
properties:(i) J = O2(H) has order 29and is of class at least 3.(ii) H/J is isomorphic to the Frobenius group of order
20.(iii) If P is a Sylow 5-subgroup of H, then
Cj(P) ⊆ Z(J).Then G = H • O(G) or G ≊
, the
simple group of Tits, as defined in [6].For the remainder of the paper, G will denote a finite
group which satisfies the hypotheses of the theorem as well as G ≠
H • O(G). Thus Glauberman's theorem
[1] can be applied to G and we have that
〈z〉 is not weakly closed in H (with
respect to G). The other notation is standard (see
[2], for example).
Publisher
Canadian Mathematical Society
Cited by
14 articles.
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