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Groups of automorphisms and centralizers

Published online by Cambridge University Press:  24 October 2008

Alexandre Turull
Alexandre Turull
Affiliation:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124, U.S.A.
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Let G be a finite solvable group and A a group of automorphisms of G such that (|A|, |G|) = 1. We denote by h(G) the Fitting height of G and by l(A) the length of the longest chain of subgroups of A. Then, under some additional hypotheses, it is known from [5] that h(G) ≤ 2l(A) + h(CG(A)) and from [8] that, when CG(A) = 1, h(G) ≤ l(A), both results being best possible (see [6, 7]). The present paper attempts to explain the difference in the coefficient of l(A) in the two inequalities, from 2 to 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 227 - 238
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

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