Commutators between coprime order elements in non-abelian simple groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910903285317632 |
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| author | Lucchini, Andrea Spiga, Pablo |
| author_facet | Lucchini, Andrea Spiga, Pablo |
| contents | Recent investigations on the set of commutators between the elements of a finite group having relatively prime orders have prompt us to propose a variant of the Ore conjecture: For every finite non-abelian simple group and for every $g\in G$, there exist $x,y\in G$ with $g=[y,x]$ and with the order of $x$ relatively prime to the order of $y$. In this note we present some evidence towards the veracity of this conjecture by proving it for alternating groups and some sporadic simple groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Commutators between coprime order elements in non-abelian simple groups Lucchini, Andrea Spiga, Pablo Group Theory Recent investigations on the set of commutators between the elements of a finite group having relatively prime orders have prompt us to propose a variant of the Ore conjecture: For every finite non-abelian simple group and for every $g\in G$, there exist $x,y\in G$ with $g=[y,x]$ and with the order of $x$ relatively prime to the order of $y$. In this note we present some evidence towards the veracity of this conjecture by proving it for alternating groups and some sporadic simple groups. |
| title | Commutators between coprime order elements in non-abelian simple groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2504.02330 |