Fixed-point free action of an abelian group of odd non-squarefree exponent

Date

2011-1-19

Author

Ercan, Gülin
Güloğlu, İsmail Ş.
Sağdiçoğlu, Öznur Mut

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AbstractLet 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.

Subject Keywords

Automorphisms of solvable groups, Non-coprime action, Fixed-point free action, Carter subgroup

URI

https://hdl.handle.net/11511/28381

Journal

Proceedings of the Edinburgh Mathematical Society

DOI

https://doi.org/10.1017/s0013091509000583

Collections

Department of Mathematics, Article

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Citation Formats

G. Ercan, İ. Ş. Güloğlu, and Ö. M. Sağdiçoğlu, “Fixed-point free action of an abelian group of odd non-squarefree exponent,” Proceedings of the Edinburgh Mathematical Society, pp. 77–89, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/28381.