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


Author: Larry Finkelstein
Journal: Proc. Amer. Math. Soc. 62 (1977), 237-241
MSC: Primary 20D05
DOI: https://doi.org/10.1090/S0002-9939-1977-0439928-2
MathSciNet review: 0439928
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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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DOI: https://doi.org/10.1090/S0002-9939-1977-0439928-2
Article copyright: © Copyright 1977 American Mathematical Society

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