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September 10, 2025Open Access

Flag‐Transitive 2‐Designs and Mathieu Group M12

Key Points

Exactly nine nonisomorphic flag-transitive 2-designs were found, enriching the existing classification framework.
These designs are characterized by their structure under the action of the Mathieu group M12.
The findings contribute significant references for the classification of designs involving other simple groups.
The discovery advances the understanding of 2-designs and their relationship with automorphism groups.

Abstract

In this paper, we announce the completion of the search for all flag‐transitive point‐primitive nontrivial 2‐designs with M 12 as the socle of their automorphism groups, and we discover that there are exactly nine of these nonisomorphic 2‐designs. This paper enriches the classification of 2‐designs and provides valuable references for addressing the classification of designs under the action of other simple groups.

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Cite This Study

Tian et al. (Wed,) studied this question.

synapsesocial.com/papers/68c1ad4f54b1d3bfb60e4c9c https://doi.org/https://doi.org/10.1155/jom/2866118

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