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THE IDENTIFICATION OF FINITE GROUPS OF PSL (5, q)-TY?E AND PSU (5, q)-TY?E MICHAEL J. COLLINSf AND RONALD M. SOLOMON 1. Introduction The Sylow 2-subgroups of the finite simple groups PSL (5, q) and PSU (5, q) for odd q fall into two classes depending on the congruence of q modulo 4. In an attempt to characterise these groups by the structure of their Sylow 2-subgroups [3], Mason has shown that a corefree group having one of these groups as Sylow 2-subgroup and having no subgroup of index 2 has a fusion pattern for its involutions and a 2-local structure which is similar to that in one of the actual groups. In particular, he was able to divide such groups into two categories according to the nonabelian composi- tion factors of the centralisers of involutions, leaving an indeterminacy over the cores and possible odd order quotients. With a definition which is given in Section 2 and analogously in Section 5, he showed that such a group was either of PSL (5, q)-type or of PSU (5, q)-type. In this paper, we shall identify these groups. THEOREM. Let q be an odd prime power, and let G be a finite
Bulletin of the London Mathematical Society – Wiley
Published: Jul 1, 1975
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