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non-coprime action

Proceedings of the Edinburgh Mathematical Society (1)

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Fixed-point free action of an abelian group of odd non-squarefree exponent
Part of
- Representation theory of groups
Gülin Ercan, İsmail Ş. Güloğlu, Öznur Mut Sağdiçoğlu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 1 / February 2011

Published online by Cambridge University Press:

19 January 2011, pp. 77-89
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Let A be a finite group acting fixed-point freely on a finite (solvable) group G. A longstanding conjecture is that if (|G|, |A|) = 1, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. It is expected that the conjecture is true when the coprimeness condition is replaced by the assumption that A is nilpotent. We establish the conjecture without the coprimeness condition in the case where A is an abelian group whose order is a product of three odd primes and where the Sylow 2-subgroups of G are abelian.