Clustering in SQL with any of a set of properties being equal - sql

Question

I have a Table T with 4 properties: {id, v, p1, p2} with id being unique.
I have to associate these items into disjunct groups g1,...,gn.
Let G := {g1,...,gn} and let gi belong to G.
For any t and t' that belongs to T and to gi, the following properties hold:
there is no t' where t.v != t'.v
there exists at least one t'' in gi, such that t.p1=t''.p1 or t.p2=t''.p2
Currently I start with the following to create the first candidates to become groups (here g):
SELECT
T.v,
T.p1,
ROW_NUMBER () OVER (ORDER BY T.v DESC, T.p1 DESC) as g
INTO TEMP t_TG
FROM T
GROUP BY T.v, T.p1
ORDER BY T.v DESC, T.p1 DESC;
In order to fetch the property p2 I use the following query:
SELECT DISTINCT
T.v,
T.p1,
T.p2,
t_TG.g
INTO TG
FROM T
JOIN t_TG ON
T.v=t_TG.v AND T.p1=t_TG.p1
Now comes the part I'm not sure about. I know that:
For each row in TG I need to find other other groups along these lines:
SELECT DISTINCT g FROM TG WHERE p2 IN (SELECT p2 FROM TG WHERE g=gi);
The result should then be updated in TG like this:
UPDATE TG SET g=gmin (minimum of previous select) WHERE g IN (result of previous select)
This needs to be done until no changes happen in the Table.
Is SLQ even the appropriate tool for this task?
If so how do I implement this last step and should I use RECURSIVE?