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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Examples of centralizers of automorphism groups


Author: Alexandre Turull
Journal: Proc. Amer. Math. Soc. 91 (1984), 537-539
MSC: Primary 20D45; Secondary 20F28
MathSciNet review: 746084
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Abstract: If $ AG$ is a finite solvable group with $ (\left\vert A \right\vert,\left\vert G \right\vert) = 1$ and $ G \triangleleft AG$, we explore the relationship between the Fitting height of $ G$, the composition length of $ A$ and the structure of $ {C_G}(A)$. For any $ A$, we give examples where the difference between the Fitting height of $ G$ and that of $ {C_G}(A)$ is exactly twice the composition length of $ A$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746084-3
PII: S 0002-9939(1984)0746084-3
Article copyright: © Copyright 1984 American Mathematical Society