Is it permissible that three or four persons share one camel as Udh-hiyah ('Eid sacrificial animal)? Must they be seven persons?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

To share one camel or cow as Udh-hiyah, it is a condition that one's share is not less than one seventh. It was narrated on the authority of Jaabir that he said, "We went out along with the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, for Hajj. He commanded that a cow or a camel is to be shared by seven people." [Muslim]

That is regarding the hady (Hajj sacrificial animal), and the same applies to the Udh-hiyah by analogy.

Thus, it is permissible that two or three or up to seven people share one cow or camel as their Udh-hiyah. It is also permissible that only one person slaughters a cow or camel as their Udh-hiyah.

Allaah Knows best.