Yes, Mexican salamanders, commonly known as axolotls (pronounced "uhk-suh-LOT-lz"), belong to the genus Ambystoma. Specifically, they are classified as Ambystoma mexicanum. This genus includes several species of tiger salamanders native to North America.
Axolotls, in particular, are unique among their peers because they are neotenic, which means they reach sexual maturity while still retaining larval or juvenile characteristics, such as their external gills. This adaptation allows them to live in environments with few predators, where they can thrive.