More of an SQL question

I already have PHP do this but I am trying to trim the code down a bit.

I have 2 tables one contains users ids and group ids, another contains group ids and group names. I want to run a querry that gets all the group ids for a specific user and then uses that result to get the group name from the other table.

So something like

SELECT group_name FROM group_table WHERE group_id = (SELECT group_id WHERE user_id=3)

Possible?

Code:

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UserGroups
- UserID
- GroupID

Groups
- GroupID
- GroupName

SELECT GroupName
FROM UserGroups
        INNER JOIN Groups ON (Groups.GroupID = UserGroups.GroupID)
WHERE UserGroup.UserID = [some number]

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