Journal article

Publication year: 1998

Pages: 1-+

Journal: Memoirs of the American Mathematical Society

Volume number: 136

Issue number: 649

ISSN: 0065-9266

Publisher: American Mathematical Society

Abstract: 

Let G be a group, p a fixed prime, I = {1,..., n} and let B and P-i, i is an element of I be a collection of finite subgroups of G. Then G satisfies P-n (with respect to p, B and P-i, i is an element of I) if: (1) G = (P-i \ i is an element of I). (2) B is the normalizer of a p-Sylowsubgroup in P-i.

(3) No nontrivial normal subgroup of B is normal in G.

(4) O-pl(P-i/O-p(Pi)) is a rank 1 Lie-type group in char p. (Also including solvable cases.)

If n = 2 then the structure of P-1, P-2 was determined by Delgado and Stellmacher [5]. In this paper we (partially) treat the case n = 3. This has applications for locally finite, chamber transitive Tits-geometries and the classification of quasithin groups.

Harvard Citation style: Stellmacher, B. and Timmesfeld, F. (1998) Rank 3 amalgams, Memoirs of the American Mathematical Society, 136(649), pp. 1-+

APA Citation style: Stellmacher, B., & Timmesfeld, F. (1998). Rank 3 amalgams. Memoirs of the American Mathematical Society. 136(649), 1-+.