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arXiv · 2312.16416

A proof of {Gross}' conjecture on $2$-automorphic $2$-groups

Cai Heng Li·Yan Zhou Zhu
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Abstract

Building upon previous results, a classification is given of finite $p$-groups of which subgroups of order $p$ are all fused. This completes the classification problem dated back to Higman 1963 on the so-called Suzuki $2$-groups, and confirms a conjecture of Gross proposed in 1974. As a consequence, two open problems on AT-groups and FIF-groups are solved.

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Cai Heng Li, Yan Zhou Zhu. 2023-12-27. A proof of {Gross}' conjecture on $2$-automorphic $2$-groups. https://doi.org/10.1112/plms.70002

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