I have one general and one specific questions.
- What is the expression for the exponent of the direct sum of finite groups?
- What is the exponent of $\sum^t_i S_{N_i} \wr D_{m_i}$?
Here, $i, N_i, m_i$ are positive integers, $S_{N_i}$ is the symmetric group over $N_i$ symbols, $D_{m_i}$ is the dihedral group of order $2 m_i$.
My effort: I guess the exponent should be the lcm of the exponent of each $S_{N_i} \wr D_{m_i}$.
Am I correct?