Greedy base sizes for sporadic simple groups
A base for a permutation group 𝐺 acting on a set Ω is a sequence ℬ of points of Ω such that the pointwise stabiliser is trivial. Denote the minimum size of a base for 𝐺 by . There is a natural greedy algorithm for constructing a base of relatively small size; denote by the maximum size of a base it...
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| Published in | Journal of group theory Vol. 28; no. 5; pp. 1079 - 1094 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.09.2025
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| Online Access | Get full text |
| ISSN | 1433-5883 1435-4446 1435-4446 |
| DOI | 10.1515/jgth-2024-0187 |
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| Summary: | A base for a permutation group 𝐺 acting on a set Ω is a sequence ℬ of points of Ω such that the pointwise stabiliser
is trivial.
Denote the minimum size of a base for 𝐺 by
.
There is a natural greedy algorithm for constructing a base of relatively small size; denote by
the maximum size of a base it produces.
Motivated by a long-standing conjecture of Cameron, we determine
for every almost simple primitive group 𝐺 with socle a sporadic simple group, showing that |
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| ISSN: | 1433-5883 1435-4446 1435-4446 |
| DOI: | 10.1515/jgth-2024-0187 |