Fixed-point free action of an abelian group of odd non-squarefree exponent
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KünyeERCAN, G., GÜLOĞLU, İ.Ş., SAĞDIÇOĞLU, Ö.M. (2011). Fixed-point free action of an abelian group of odd non-squarefree exponent. Proceedings of the Edinburgh Mathematical Society (Series 2), 54 (1), pp 77-89. https://dx.doi.org/10.1017/S0013091509000583.
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.