Locally nilpotent 4-Engel groups are Fitting groups

Gunnar Traustason

doi:10.1016/j.jalgebra.2003.07.012

Locally nilpotent 4-Engel groups are Fitting groups

Gunnar Traustason

Mathematics (Faculty of Engineering)

Research output: Contribution to journal › Article › peer-review

Abstract

Let G be a locally nilpotent 4-Engel group. We show that the normal closure of any element from G is nilpotent of class at most 4. When G has no element of order 2 or 5, the normal closure has class at most 3. These bounds are sharp. (C) 2003 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	41482
Journal	Journal of Algebra
Volume	270
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2003.07.012
Publication status	Published - 2003

Subject classification (UKÄ)

Mathematical Sciences

Free keywords

Engel groups
locally nilpotent groups
Fitting groups

Access to Document

10.1016/j.jalgebra.2003.07.012

Cite this

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title = "Locally nilpotent 4-Engel groups are Fitting groups",

abstract = "Let G be a locally nilpotent 4-Engel group. We show that the normal closure of any element from G is nilpotent of class at most 4. When G has no element of order 2 or 5, the normal closure has class at most 3. These bounds are sharp. (C) 2003 Elsevier Inc. All rights reserved.",

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AB - Let G be a locally nilpotent 4-Engel group. We show that the normal closure of any element from G is nilpotent of class at most 4. When G has no element of order 2 or 5, the normal closure has class at most 3. These bounds are sharp. (C) 2003 Elsevier Inc. All rights reserved.

KW - Engel groups

KW - locally nilpotent groups

KW - Fitting groups

U2 - 10.1016/j.jalgebra.2003.07.012

DO - 10.1016/j.jalgebra.2003.07.012

M3 - Article

SN - 0021-8693

VL - 270

SP - 41482

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Locally nilpotent 4-Engel groups are Fitting groups

Abstract

Subject classification (UKÄ)

Free keywords

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Cite this