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This is a Quantitative Study study.

October 16, 2025Open Access

Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps

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Finite 2-groups with specific subgroup structures demonstrate unique automorphism groups, enhancing group theory's depth.
The classification includes pairs of finite 2-groups and arc-transitive maps, pinpointing the importance of Euler characteristics.
Understanding these structures aids in broader applications in algebra and geometry, revealing interconnections in group theory.
The study's classification is essential for future research in symmetry and group actions, particularly in combinatorial contexts.

Implication

This classification reveals structures of finite 2-groups with specific subgroup types, and identifies arc-transitive maps.

Abstract

We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs (G,M), such that G is a finite 2-group and M is a G-arc-transitive map with Euler characteristic not being divisible by 4.

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Cite This Study

Peice Hua (2025) studied this question.

synapsesocial.com/papers/68f0f51d8dd8ea469b1d71ad https://doi.org/10.48550/arxiv.2508.05981

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Implication

This classification reveals structures of finite 2-groups with specific subgroup types, and identifies arc-transitive maps.

Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps

Key Points

Implication

Abstract

Discussion

Cite This Study

Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps

Key Points

Implication

Abstract

Discussion

Cite This Study

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