On the Fitting length conjecture
type: Item
instance of: scholarly article
title: On the Fitting length conjecture
zbMATH Open document ID: 0654.20015
DOI: 10.1007/BF01199810
author: Alberto Espuelas
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: The longstanding Fitting length conjecture asserts the following: Let A be a solvable group acting on the solvable group G. Assume that \((| A|,| G|)=1\) and \(C_ G(A)=1\). Then the Fitting length of G is at most the composition length of A. The bound is best possible. The conjecture was only known for some supersolvable groups A [see \textit{A. Turull}, J. Reine Angew. Math. 371, 67-91 (1986; Zbl 0587.20017)]. Here it is proved for groups of odd order A satisfying the following: (i) If \(p,q\in \pi (A)\), then \(p\nmid q-1\). (ii) If \(| G|\) is even and \(p\in \pi (A)\), then \(p| 2^ k+1\) for some \(k>1\). Observe that (ii) is slightly stronger than assuming that p is not a Mersenne prime.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 4067183
zbMATH Keywords: Fitting length conjecture
zbMATH Keywords: solvable group
zbMATH Keywords: composition length
zbMATH Keywords: groups of odd order
Wikidata QID: Q123010167
MaRDI profile type: Publication
cites work: Regular orbits on symplectic modules
cites work: Trivial Set-Stabilizers in Finite Permutation Groups
cites work: Fixed point free action with regular orbits.
description: scientific article; zbMATH DE number 4067183