On finite groups admitting a fixed point free abelian operator group whose order is a product of three primes

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2009
Mut Sağdıçoğlu, Öznur
A long-standing conjecture states that if A is a finite group acting fixed point freely on a finite solvable group G of order coprime to jAj, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. If A is nilpotent, it is expected that the conjecture is true without the coprimeness condition. We prove that the conjecture without the coprimeness condition is true when A is a cyclic group whose order is a product of three primes which are coprime to 6 and the Sylow 2-subgroups of G are abelian. We also prove that the conjecture without the coprimeness condition is true when A is an abelian group whose order is a product of three primes which are coprime to 6 and jGj is odd.

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Citation Formats
Ö. Mut Sağdıçoğlu, “On finite groups admitting a fixed point free abelian operator group whose order is a product of three primes,” Ph.D. - Doctoral Program, Middle East Technical University, 2009.