On a Fitting length conjecture without the coprimeness condition

Ercan, Gülı̇n

doi:10.1007/s00605-011-0287-3

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…Let A = ϕ be a cyclic group acting on a solvable group G. In that case, the problem of finding a bound for h(G) in terms of |A| and |C G (A)| is still open (see the Kourovka Notebook [7, 13.8(a)]). However, there are some nice bounds proved in the case that the action is fixed point free, that is, when C G (A)=1: Under some further assumptions on the structure of A and G, a linear bound has been obtained for h(G) depending on l(A) in [2,3], and [8]. A current article established a quadratic bound h(G) ≤ 7l(A) 2 without any further assumptions on A or G (see [6,Corollary 1.2]).…”

Section: Question 17 Under the Hypothesis Of Theorem E Is F(g A) Boun...mentioning

confidence: 99%

A Fitting height lemma and its applications

Kızmaz

2021

Arch. Math.

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Let A be a group acting on a solvable group G and let N be an We prove the inequality h([G, A]) ≤ h([G, A]N/N ) + h([N, A])where h(G) denotes the Fitting height of G. As an application of this result, we obtain several Fitting height inequalities. A new concept "fixed point free separability" and a new characteristic subgroup Y (G) is defined and used in order to prove some further results about the Fitting height of a group. In the last section, a new characterization of solvable groups is given: a group G is solvable if and only if it is fixed point free separable.

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Section: Question 17 Under the Hypothesis Of Theorem E Is F(g A) Boun...mentioning

confidence: 99%

A Fitting height lemma and its applications

Kızmaz

2021

Arch. Math.

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“…For example, it has been proved when A is cyclic of order a product of two and three distinct primes by K. Cheng [2] and G. Ercan and İ. Güloğlu [5] respectively. Further work has been done by G. Ercan in [3], where A is cyclic of order p n q for primes p and q greater than 3 and n ∈ N.…”

Section: Introductionmentioning

confidence: 98%

On fixed-point-free automorphisms

Collins

Flavell

2015

Journal of Algebra

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“…Unlike the aforementioned "linear" results in the coprime case, the bound in Dade's theorem is exponential. Improving this bound to a linear one is a difficult problem; it was tackled in some special cases by Ercan and Güloglu [21,22,23].…”

Section: Introductionmentioning

confidence: 99%

On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order

Khukhro

2015

Sib Math J

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Abstract. It is proved that if a finite p-soluble group G admits an automorphism ϕ of order p n having at most m fixed points on every ϕ-invariant elementary abelian p ′ -section of G, then the p-length of G is bounded above in terms of p n and m; if in addition the group G is soluble, then the Fitting height of G is bounded above in terms of p n and m. It is also proved that if a finite soluble group G admits an automorphism ψ of order p a q b for some primes p, q, then the Fitting height of G is bounded above in terms of |ψ| and |C G (ψ)|.

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On a Fitting length conjecture without the coprimeness condition

Cited by 7 publications

References 11 publications

A Fitting height lemma and its applications

A Fitting height lemma and its applications

On fixed-point-free automorphisms

On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order

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