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ABSTRACr. Let G be a finite group with 0 (G) = 1, A a standard component of G and X the normal closure of A in G. Furthermore, assume that C(A) has cyclic Sylow 2-subgroups. Then conditions are given on A which imply that either X = A or C (A) has Sylow 2-subgroups of order 2. These results are then applied to the cases where A is isomorphic to * 0 or Ru, the proper 2-fold covering of the Rudvalis group.

Finite groups with a standard component whose centralizer has cyclic Sylow 2-subgroups