On a Fitting length conjecture without the coprimeness condition.
type: Item
instance of: scholarly article
title: On a Fitting length conjecture without the coprimeness condition.
zbMATH Open document ID: 1263.20023
author: Gülin Ercan
published in: Monatshefte für Mathematik
publication date: 2012-11-21T00:00:00Z
review text: Let \(G\) be a finite solvable group, let \(A\) be a nilpotent group of automorphisms of \(G\), and assume that \(C_G(A)=1\). It is conjectured that then the Fitting height \(h(G)\) of \(G\) is bounded above by the length \(\ell(A)\) of the longest chain of subgroups of \(A\). While this is known to be true in many cases, the conjecture is still open in general. Recent results include [\textit{G. Ercan} and \textit{İ. Ş. Güloğlu}, J. Algebra 320, No. 1, 426-436 (2008; Zbl 1155.20021) and \textit{G. Ercan, İ. Ş. Güloğlu} and \textit{Ö. M. Sağdiçoğlu}, Proc. Edinb. Math. Soc., II. Ser. 54, No. 1, 77-89 (2011; Zbl 1216.20009)]. In the present paper, the authors prove this conjecture when \(A\) is cyclic of order \(p^nq\), \(p\) and \(q\) primes coprime to \(6\), and \(G\) has Abelian Sylow \(2\)-subgroups.
reviewed by: Alexandre Turull
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 6109327
zbMATH Keywords: finite solvable groups
zbMATH Keywords: Fitting heights
zbMATH Keywords: Fitting lengths
zbMATH Keywords: fixed point free actions
zbMATH Keywords: representations
MaRDI profile type: Publication
full work available at URL: s00605-011-0287-3
OpenAlex ID: W2027662783
Wikidata QID: Q123290216
cites work: A NOTE ON FIXED-POINT-FREE ACTIONS OF FINITE GROUPS
cites work: Finite groups admitting fixed point free automorphisms of order pq
cites work: Carter subgroups and Fitting heights of finite solvable groups
cites work: Finite groups admitting fixed-point free automorphisms of order pqr
cites work: Fixed point free action on groups of odd order.
cites work: Fixed-point free action of an abelian group of odd non-squarefree exponent
cites work: The Fitting length of the Hughes subgroup
cites work: Q3934684
cites work: On groups admitting fixed point free abelian operator groups
cites work: Fitting height of groups and of fixed points
cites work: Q4856489
DOI: 10.1007/S00605-011-0287-3
description: scientific article; zbMATH DE number 6109327