The maximal rank of a string group generated by involutions for alternating groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918120133754880 |
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| author | Anzanello, Jessica Fernandes, Maria Elisa Spiga, Pablo |
| author_facet | Anzanello, Jessica Fernandes, Maria Elisa Spiga, Pablo |
| contents | A string group generated by involutions, or SGGI, is a pair $Γ=(G, S)$, where $G$ is a group and $S=\{ρ_0,\ldots, ρ_{r-1}\}$ is an ordered set of involutions generating $G$ and satisfying the commuting property: $$\forall i,j\in\{0,\ldots, r-1\}, \;|i-j|\ne 1\Rightarrow (ρ_iρ_j)^2=1.$$ When $S$ is an independent set, the rank of $Γ$ is the cardinality of $S$. We determine an upper bound for the rank of an SGGI over the alternating group of degree $n$. Our bound is tight when $n\equiv 0,1,4\pmod 5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The maximal rank of a string group generated by involutions for alternating groups Anzanello, Jessica Fernandes, Maria Elisa Spiga, Pablo Group Theory Combinatorics A string group generated by involutions, or SGGI, is a pair $Γ=(G, S)$, where $G$ is a group and $S=\{ρ_0,\ldots, ρ_{r-1}\}$ is an ordered set of involutions generating $G$ and satisfying the commuting property: $$\forall i,j\in\{0,\ldots, r-1\}, \;|i-j|\ne 1\Rightarrow (ρ_iρ_j)^2=1.$$ When $S$ is an independent set, the rank of $Γ$ is the cardinality of $S$. We determine an upper bound for the rank of an SGGI over the alternating group of degree $n$. Our bound is tight when $n\equiv 0,1,4\pmod 5$. |
| title | The maximal rank of a string group generated by involutions for alternating groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2505.09169 |