### Abstract

We know that every element in an Alternating group An, n ≥ 5, can be written as a Engel word of length two (Carracedo, Extracta Math. 30(2), 251–262, 2015 and J. Algebra Appl. 16(2), 1750021, 10 p., 2017). There is a conjecture that every element in an Alternating group An, n ≥ 5, can be written as an Engel word of arbitrary length. We give here a computational approach to this problem, what allows to prove the conjecture for 5 ≤ n ≤ 14.

Original language | English |
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Title of host publication | Computational Mathematics, Numerical Analysis and Applications |

Subtitle of host publication | Lecture Notes of the XVII 'Jacques-Louis Lions' Spanish-French School |

Publisher | Springer Cham |

Volume | 13 |

Edition | 1 |

ISBN (Electronic) | 978-3-319-49631-3 |

ISBN (Print) | 978-3-319-49630-6 |

Publication status | Published - 2017 |

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## Profiles

## Jorge Martinez Carracedo

- School of Computing - Lecturer in Computer Science (Internet of Things
- Faculty Of Computing, Eng. & Built Env. - Lecturer

Person: Academic

## Cite this

Martinez Carracedo, J., & Martinez Lopez, C. (2017). A Computational Approach to Verbal Width in Alternating Groups. In

*Computational Mathematics, Numerical Analysis and Applications: Lecture Notes of the XVII 'Jacques-Louis Lions' Spanish-French School*(1 ed., Vol. 13). Springer Cham.