September 28, 2025Open Access

On transitive permutation groups with exponential graph growth

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Authors

DMDjordje MitrovićUniversity of Auckland GVGabriel VerretUniversity of Auckland

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Implication

The findings reveal exponential graph growth in transitive permutation groups with nontrivial stabilisers, suggesting broader implications for $L$-pairs.

Key Points

The graph growth of a locally-$L$ pair $(Γ,G)$ is shown to be exponential under certain conditions.
A key condition is the existence of a nontrivial block $B$, where $L$ has a nontrivial pointwise stabiliser on $Ω\setminus B$.
This research generalizes existing literature on transitive permutation groups with exponential growth.
Understanding graph growth can enhance insights into the structure of permutation groups.

Cite This Study

Mitrović et al. (2025) studied this question.

synapsesocial.com/papers/68d913a34ddcf71ba560ba7c https://doi.org/10.48550/arxiv.2508.12588

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Implication

The findings reveal exponential graph growth in transitive permutation groups with nontrivial stabilisers, suggesting broader implications for $L$-pairs.

On transitive permutation groups with exponential graph growth

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Member takes

Implication

Key Points

Cite This Study

On transitive permutation groups with exponential graph growth

Discussion

Member takes

Implication

Key Points

Cite This Study

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