$GL_n(\mathbb{F}_q)$-analogues of some properties of $n$-cycles in $\mathfrak{S}_n$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914891884920832 |
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| author | Lewis, Joel Brewster |
| author_facet | Lewis, Joel Brewster |
| contents | We give analogues in the finite general linear group of two elementary results concerning long cycles and transpositions in the symmetric group: first, that the long cycles are precisely the elements whose minimum-length factorizations into transpositions yield a generating set, and second, that a long cycle together with an appropriate transposition generates the whole symmetric group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $GL_n(\mathbb{F}_q)$-analogues of some properties of $n$-cycles in $\mathfrak{S}_n$ Lewis, Joel Brewster Group Theory Combinatorics We give analogues in the finite general linear group of two elementary results concerning long cycles and transpositions in the symmetric group: first, that the long cycles are precisely the elements whose minimum-length factorizations into transpositions yield a generating set, and second, that a long cycle together with an appropriate transposition generates the whole symmetric group. |
| title | $GL_n(\mathbb{F}_q)$-analogues of some properties of $n$-cycles in $\mathfrak{S}_n$ |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2407.20347 |