The structure that is not involved in the reproduction of at least one major group of fungi is a fruiting body.

Here's why:

* Fruiting bodies are structures that produce spores for sexual reproduction. Many fungi, like mushrooms and toadstools, rely on fruiting bodies for this purpose.

* However, some fungal groups reproduce asexually, and they might not develop fruiting bodies. For example, yeasts reproduce through budding, which is an asexual process.

Let me know if you'd like more details on fungal reproduction!