Abstract
0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 1 Statement of the main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 2 Higher dimensional subgroups of O(n + 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 3 Higher dimensional transformation groups on homology spheres, geometric weight systems and orbit structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 4 Higher dimensional transformation groups on homotopy spheres and the proof of Theorem B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 5 Degree of symmetry of exotic spheres revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 6 Large transformation groups on exotic spheres in bP.+ 1 . . . . . . . . . . . . . . . . . . . . . . . . . 384
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