You are thinking of the word abbey, but that is not the correct answer.
The word does not refer to a single building, but an entire complex of buildings within a walled precinct, often with farming complexes (granges) and small monastic communities (cells) spread further away from the main site.
An abbey was generally a larger monastery for monks with an Abbot in charge. Smaller monasteries would have a Prior in charge and were called priories.
Nuns generally lived in a convent with an Abbess or Prioress in charge, again depending on the size of the convent. In some rare cases the convent might be called an abbey or priory.
Any group of Buddhists (Monks/Nuns or lay people) who study and practice together is called a Sangha. If they lived together in a monastic setting then the building is called a monastery.
Monks - monastery. Nuns - convent.
monastery, priory
There is no known special name for a group of monks. A monk is a singular term and when multiple monks are present an "s" is added to make the word monk plural which is monks.
A religious community of nuns is a convent.
Monastery for monks (males).Nunnery or convent for nuns (females).
monasteries- the dwelling place of a community of monks
Sangha
allowed monks to adapt to rural conditions
Normally it would be called a monastery, although it can also be an Abbey, a Priory, or a Rectory, or even an Archabbey in the case of St. Vincent Archabbey in Latrobe, Pennsylvania; depending on the specific circumstances. There are also several groups of monks, like the Camaldolese and the Carthusians who live in hermitages.
Hermits usually live alone and isolated from a community. Monks live in monasteries, usually with other monks.
Monasteries or temples (communities of monks) usually are supported by donations, contributions, and/or begging.