The non-synchronizing primitive groups of degree up to 624
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912156635627520 |
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| author | Soicher, Leonard H. |
| author_facet | Soicher, Leonard H. |
| contents | We describe the methods and results of a classification of the non-synchronizing primitive permutation groups of degree up to 624. We make use of theory and computation to determine the primitive groups of degree up to 624 that are non-separating, which is a necessary, and very often sufficient, condition for a primitive group to be non-synchronizing, and determine exactly which of these non-separating groups are non-synchronizing. A new infinite sequence of non-synchronizing graphs is discovered and new examples of non-separating, but synchronizing, groups are found. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10903 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The non-synchronizing primitive groups of degree up to 624 Soicher, Leonard H. Group Theory 20B15 (Primary) 05-08, 05C15, 05C69, 20-08, 20B25 (Secondary) We describe the methods and results of a classification of the non-synchronizing primitive permutation groups of degree up to 624. We make use of theory and computation to determine the primitive groups of degree up to 624 that are non-separating, which is a necessary, and very often sufficient, condition for a primitive group to be non-synchronizing, and determine exactly which of these non-separating groups are non-synchronizing. A new infinite sequence of non-synchronizing graphs is discovered and new examples of non-separating, but synchronizing, groups are found. |
| title | The non-synchronizing primitive groups of degree up to 624 |
| topic | Group Theory 20B15 (Primary) 05-08, 05C15, 05C69, 20-08, 20B25 (Secondary) |
| url | https://arxiv.org/abs/2412.10903 |