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

Finkelstein, Larry

doi:10.1090/S0002-9939-1977-0439928-2

Finite groups with a standard component whose centralizer has cyclic Sylow $2$-subgroups
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Proc. Amer. Math. Soc. 62 (1977), 237-241 Request permission

Abstract:

Let G be a finite group with $O(G) = 1$, 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 $\cdot 0$ or Ru, proper 2-fold covering of the Rudvalis group.

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Standard components of alternating type centralized by a

group

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