[math] \newcommand{\mathds}{\mathbb}[/math]

Work out the theory of the subgroups of [math]O_N,U_N[/math] constructed via

[[math]] (\det U)^d=1 [[/math]]

with [math]d\in\mathbb N\cup\{\infty\}[/math], which generalize both [math]O_N,U_N[/math] and [math]SO_N,SU_N[/math].