I learnt that subgroup of free group is still a free group.
How far can we generalize this?
In particular, is a subgroup of free product of cyclic groups, eg. $$\mathbb{Z}*\mathbb{Z}*\dots *\mathbb{Z}_{n_1}*\dots *\mathbb{Z}_{n_k}$$ still a free product of cyclic groups?
Thanks a lot.