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

Key Points

• 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.