PreprintCC BY 4.0arXiv
Mathieu groups as flag-transitive automorphism groups of block designs
Abstract
In this article, we study $2−(v,k,λ)$ designs 𝒟 admitting a flag-transitive almost simple automorphism group G with socle one of the Mathieu groups. In conclusion, we obtain all such $2$-designs with explicit constructions with appropriate references to known designs. To our knowledge, we obtain $101$ newly-constructed flag-transitive $2$-designs.
Related
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- Transitive automorphism groups of maximal curves
- On the lengths of MDS codes with a two-transitive permutation automorphism group
- Reduction for flag-transitive symmetric 2-designs with gcd(k, λ) = p
- The Mathieu Property for Compact Connected Lie Groups
BibTeX
@misc{bakhtiari2026mathieu,
title = {{Mathieu groups as flag-transitive automorphism groups of block designs}},
author = {Fatemeh Bakhtiari and Ashraf Daneshkhah},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16756},
eprint = {2609.16756},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16756},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mathieu groups as flag-transitive automorphism groups of block designs
AU - Fatemeh Bakhtiari
AU - Ashraf Daneshkhah
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16756
UR - https://arxiv.org/abs/2609.16756
AB - In this article, we study $2−(v,k,λ)$ designs 𝒟 admitting a flag-transitive almost simple automorphism group G with socle one of the Mathieu groups. In conclusion, we obtain all such $2$-designs with explicit constructions with appropriate references to known designs. To our knowledge, we obtain $101$ newly-constructed flag-transitive $2$-designs.
ER -