Relying on the main results of [GT], we classify all unitary $t$-groups for $t \geq 2$ in any dimension $d \geq 2$. We also show that there is essentially a unique unitary 4-group, which is also a unitary 5-group, but not a unitary $t$-group for any $t \geq 6$.
The research of the second and third authors is partially supported by the Spanish Ministerio de Educación y Ciencia proyecto MTM2016-76196-P and Prometeo Generalitat Valenciana. The fourth author gratefully acknowledges the support of the NSF (grant DMS-1840702) and the Joshua Barlaz Chair in Mathematics. The paper is partially based upon work supported by the NSF under grant DMS-1440140 while the second, third, and fourth authors were in residence at MSRI (Berkeley, CA), during the Spring 2018 semester. It is a pleasure to thank the Institute for the hospitality and support. The first author thanks TGMRC in China Three Gorges University for the hospitality and support when he visited there in Sept–Oct 2018.
"Unitary $t$-groups." J. Math. Soc. Japan 72 (3) 909 - 921, July, 2020. https://doi.org/10.2969/jmsj/82228222