Hidden symmetry in the biased Dicke model

The symmetry operators generating the hidden $\mathbb{Z}_2$ of asymmetric quantum Rabi model (AQRM) at bias $\epsilon \in \frac{1}{2}\mathbb{Z}$ have recently been constructed by V. Mangazeev et al. [J. Phys. A: Math. Theor. 54 12LT01 (2021)]. We start with this result to determine for $N$-qubit generalisation AQRM, also known as biased Dicke model, special biases. prove general $N$ that operators, which commute Hamiltonian generate a symmetry.