On a Fitting length conjecture without the coprimeness condition
MONATSHEFTE FUR MATHEMATIK, cilt.167, ss.175-187, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 167
- Basım Tarihi: 2012
- Doi Numarası: 10.1007/s00605-011-0287-3
- Dergi Adı: MONATSHEFTE FUR MATHEMATIK
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.175-187
- Anahtar Kelimeler: Automorphisms of solvable groups, Noncoprime action, Fixedpoint free action, POINT FREE AUTOMORPHISMS, FINITE-GROUPS, SOLVABLE GROUPS
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
Let A be a finite nilpotent group acting fixed point freely by automorphisms on the finite solvable group G. It is conjectured that the Fitting length of G is bounded by the number of primes dividing the order of A, counted with multiplicities. The main result of this paper shows that the conjecture is true in the case where A is cyclic of order p (n) q, for prime numbers p and q coprime to 6 and G has abelian Sylow 2-subgroups.