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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2025-08-01
|
| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360725500122 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849229059713662976 |
|---|---|
| author | Ilia Ponomarenko Saveliy V. Skresanov Andrey V. Vasil’ev |
| author_facet | Ilia Ponomarenko Saveliy V. Skresanov Andrey V. Vasil’ev |
| author_sort | Ilia Ponomarenko |
| collection | DOAJ |
| description | 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]. |
| format | Article |
| id | doaj-art-ea13ebb71e6c4890a007d1f4e37cb1a8 |
| institution | Kabale University |
| issn | 1664-3607 1664-3615 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj-art-ea13ebb71e6c4890a007d1f4e37cb1a82025-08-22T07:46:43ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152025-08-01150210.1142/S1664360725500122Closures of permutation groups with restricted nonabelian composition factorsIlia Ponomarenko0Saveliy V. Skresanov1Andrey V. Vasil’ev2St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg 191023, RussiaNovosibirsk State University, Novosibirsk 630090, RussiaNovosibirsk State University, Novosibirsk 630090, RussiaGiven 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].https://www.worldscientific.com/doi/10.1142/S1664360725500122Permutation groupAlt-free groupk-closure |
| spellingShingle | Ilia Ponomarenko Saveliy V. Skresanov Andrey V. Vasil’ev Closures of permutation groups with restricted nonabelian composition factors Bulletin of Mathematical Sciences Permutation group Alt-free group k-closure |
| title | Closures of permutation groups with restricted nonabelian composition factors |
| title_full | Closures of permutation groups with restricted nonabelian composition factors |
| title_fullStr | Closures of permutation groups with restricted nonabelian composition factors |
| title_full_unstemmed | Closures of permutation groups with restricted nonabelian composition factors |
| title_short | Closures of permutation groups with restricted nonabelian composition factors |
| title_sort | closures of permutation groups with restricted nonabelian composition factors |
| topic | Permutation group Alt-free group k-closure |
| url | https://www.worldscientific.com/doi/10.1142/S1664360725500122 |
| work_keys_str_mv | AT iliaponomarenko closuresofpermutationgroupswithrestrictednonabeliancompositionfactors AT saveliyvskresanov closuresofpermutationgroupswithrestrictednonabeliancompositionfactors AT andreyvvasilev closuresofpermutationgroupswithrestrictednonabeliancompositionfactors |