In:
Canadian Journal of Mathematics, Canadian Mathematical Society, Vol. 24, No. 4 ( 1972-08), p. 672-685
Abstract:
In [6], J. Tits has shown that the Ree group 2 F 4 (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 = C G (z) has the following
properties: (i) J = O 2 (H) has order 2 9 and 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
C j (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).
Type of Medium:
Online Resource
ISSN:
0008-414X
,
1496-4279
DOI:
10.4153/CJM-1972-063-0
Language:
English
Publisher:
Canadian Mathematical Society
Publication Date:
1972
detail.hit.zdb_id:
1467410-5
detail.hit.zdb_id:
280533-9
