Left 3-Engel elements in locally finite 2-groups

Anastasia Hadjievangelou; Gunnar Traustason

doi:10.1080/00927872.2021.1931265

Left 3-Engel elements in locally finite 2-groups

Anastasia Hadjievangelou, Gunnar Traustason

Department of Mathematical Sciences

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

2 Citations (SciVal)

Abstract

We give an infinite family of examples that generalize the construction given by Noce, Tracey and Traustason of a locally finite 2-group G containing a left 3-Engel element x where (Formula presented.) the normal closure of x in G, is not nilpotent. The construction is based on a family of Lie algebras that are of interest in their own right and make use of a classical theorem of Lucas, regarding when (Formula presented.) is even.

Original language	English
Pages (from-to)	4869-4882
Number of pages	14
Journal	Communications in Algebra
Volume	49
Issue number	11
Early online date	5 Jun 2021
DOIs	https://doi.org/10.1080/00927872.2021.1931265
Publication status	Published - 31 Dec 2021

Bibliographical note

Funding Information:
The first author is partially supported by ‘The Norton Scholarship’. We acknowledge the EPSRC (grant number 16523160) for support. Moreover, we would like to thank Marialaura Noce for drawing our attention to Lucas’ Theorem.

Keywords

Engel elements
Lie algebras
locally finite groups

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1080/00927872.2021.1931265Licence: CC BY-NC-ND

Cite this

@article{ecceb337ec174f29a47b3d5338d4105e,

title = "Left 3-Engel elements in locally finite 2-groups",

abstract = "We give an infinite family of examples that generalize the construction given by Noce, Tracey and Traustason of a locally finite 2-group G containing a left 3-Engel element x where (Formula presented.) the normal closure of x in G, is not nilpotent. The construction is based on a family of Lie algebras that are of interest in their own right and make use of a classical theorem of Lucas, regarding when (Formula presented.) is even.",

keywords = "Engel elements, Lie algebras, locally finite groups",

author = "Anastasia Hadjievangelou and Gunnar Traustason",

note = "Funding Information: The first author is partially supported by {\textquoteleft}The Norton Scholarship{\textquoteright}. We acknowledge the EPSRC (grant number 16523160) for support. Moreover, we would like to thank Marialaura Noce for drawing our attention to Lucas{\textquoteright} Theorem. ",

year = "2021",

month = dec,

day = "31",

doi = "10.1080/00927872.2021.1931265",

language = "English",

volume = "49",

pages = "4869--4882",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis",

number = "11",

}

TY - JOUR

T1 - Left 3-Engel elements in locally finite 2-groups

AU - Hadjievangelou, Anastasia

AU - Traustason, Gunnar

N1 - Funding Information: The first author is partially supported by ‘The Norton Scholarship’. We acknowledge the EPSRC (grant number 16523160) for support. Moreover, we would like to thank Marialaura Noce for drawing our attention to Lucas’ Theorem.

PY - 2021/12/31

Y1 - 2021/12/31

N2 - We give an infinite family of examples that generalize the construction given by Noce, Tracey and Traustason of a locally finite 2-group G containing a left 3-Engel element x where (Formula presented.) the normal closure of x in G, is not nilpotent. The construction is based on a family of Lie algebras that are of interest in their own right and make use of a classical theorem of Lucas, regarding when (Formula presented.) is even.

AB - We give an infinite family of examples that generalize the construction given by Noce, Tracey and Traustason of a locally finite 2-group G containing a left 3-Engel element x where (Formula presented.) the normal closure of x in G, is not nilpotent. The construction is based on a family of Lie algebras that are of interest in their own right and make use of a classical theorem of Lucas, regarding when (Formula presented.) is even.

KW - Engel elements

KW - Lie algebras

KW - locally finite groups

UR - http://www.scopus.com/inward/record.url?scp=85107472385&partnerID=8YFLogxK

U2 - 10.1080/00927872.2021.1931265

DO - 10.1080/00927872.2021.1931265

M3 - Article

SN - 0092-7872

VL - 49

SP - 4869

EP - 4882

JO - Communications in Algebra

JF - Communications in Algebra

IS - 11

ER -

Left 3-Engel elements in locally finite 2-groups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Left 3-Engel Elements in Groups

Cite this

Left 3-Engel elements in locally finite 2-groups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Left 3-Engel Elements in Groups

Cite this