A Proof of Gross' Conjecture on $2$-Automorphic $2$-Groups

Cai Heng Li, Yan Zhou Zhu

Published 2023-12-27Version 1

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.