Closures of permutation groups with restricted nonabelian composition factors
Given a permutation group G on a finite set [Formula: see text], let [Formula: see text] denote the k-closure of G, that is, the largest permutation group on [Formula: see text] having the same orbits in the induced action on [Formula: see text] as G. Recall that a group is [Formula: see text]-free...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2025-08-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360725500122 |
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| Summary: | Given a permutation group G on a finite set [Formula: see text], let [Formula: see text] denote the k-closure of G, that is, the largest permutation group on [Formula: see text] having the same orbits in the induced action on [Formula: see text] as G. Recall that a group is [Formula: see text]-free if it does not contain a section isomorphic to the alternating group of degree d. Motivated by some problems in computational group theory, we prove that the k-closure of an [Formula: see text]-free group is again [Formula: see text]-free for [Formula: see text] and [Formula: see text]. |
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| ISSN: | 1664-3607 1664-3615 |