A Computational Approach to Verbal Width for Engel Words in Alternating Groups

A Computational Approach to Verbal Width for Engel Words in Alternating Groups

It is known that every element in the alternating group <inline-formula> <math display="inline"> <semantics> <msub> <mi>A</mi> <mi>n</mi> </msub> </semantics> </math> </inline-formula>, with <inline-formula> <...

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Main Author: Jorge Martínez Carracedo
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Symmetry
Subjects:
group theory
symmetry
Engel words
alternating group
Online Access:https://www.mdpi.com/2073-8994/11/7/877
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spelling doaj-b6d1ab186ead45c0bd3a09a6ad57d6672020-11-25T02:48:04ZengMDPI AGSymmetry2073-89942019-07-0111787710.3390/sym11070877sym11070877A Computational Approach to Verbal Width for Engel Words in Alternating GroupsJorge Martínez Carracedo0School of Computing, Jordanstown Campus, Ulster University, Northern Ireland BT37 0QB, UKIt is known that every element in the alternating group <inline-formula> <math display="inline"> <semantics> <msub> <mi>A</mi> <mi>n</mi> </msub> </semantics> </math> </inline-formula>, with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>&#8805;</mo> <mn>5</mn> </mrow> </semantics> </math> </inline-formula>, can be written as a product of at most two Engel words of arbitrary length. However, it is still unknown if every element in an alternating group is an Engel word of Arbitrary length. In this paper, a different approach to this problem is presented, getting new results for small alternating groups.https://www.mdpi.com/2073-8994/11/7/877group theorysymmetryEngel wordsalternating group
collection DOAJ
language English
format Article
sources DOAJ
author Jorge Martínez Carracedo
spellingShingle Jorge Martínez Carracedo
A Computational Approach to Verbal Width for Engel Words in Alternating Groups
Symmetry
group theory
symmetry
Engel words
alternating group
author_facet Jorge Martínez Carracedo
author_sort Jorge Martínez Carracedo
title A Computational Approach to Verbal Width for Engel Words in Alternating Groups
title_short A Computational Approach to Verbal Width for Engel Words in Alternating Groups
title_full A Computational Approach to Verbal Width for Engel Words in Alternating Groups
title_fullStr A Computational Approach to Verbal Width for Engel Words in Alternating Groups
title_full_unstemmed A Computational Approach to Verbal Width for Engel Words in Alternating Groups
title_sort computational approach to verbal width for engel words in alternating groups
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-07-01
description It is known that every element in the alternating group <inline-formula> <math display="inline"> <semantics> <msub> <mi>A</mi> <mi>n</mi> </msub> </semantics> </math> </inline-formula>, with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>&#8805;</mo> <mn>5</mn> </mrow> </semantics> </math> </inline-formula>, can be written as a product of at most two Engel words of arbitrary length. However, it is still unknown if every element in an alternating group is an Engel word of Arbitrary length. In this paper, a different approach to this problem is presented, getting new results for small alternating groups.
topic group theory
symmetry
Engel words
alternating group
url https://www.mdpi.com/2073-8994/11/7/877
work_keys_str_mv AT jorgemartinezcarracedo acomputationalapproachtoverbalwidthforengelwordsinalternatinggroups
AT jorgemartinezcarracedo computationalapproachtoverbalwidthforengelwordsinalternatinggroups
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