We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of inhomogeneous wreath products. In the proof, we combine techniques from combinatorics, group theory, and geometry. Our result significantly improves the Babai's description (1975).

中文翻译：

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平面图自同构群的 Jordan-like 表征

我们研究平面图的自同构群。主要结果是对所有抽象群的完整递归描述，这些抽象群可以实现为平面图的自同构群。表征是根据不均匀的花环产品制定的。在证明中，我们结合了组合学、群论和几何学的技术。我们的结果显着改进了 Babai 的描述 (1975)。