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.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/3/12610990/index.pdf |
| Date | 01 August 2009 |
| Creators | Mut Sagdicoglu, Oznur |
| Contributors | Ercan, Gulin |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | Access forbidden for 1 year |
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