Seems like you want to get Distinct on one column.
Hoping ur using SQL Server 2005 or Above
Select First_Name,Last_Name,P_Id
FROM
(
Select First_Name,Last_Name,P_Id
Row_Number() Over (Partition By P_Id Order By First_Name) As RNum
From Table1) T1
WHERE T1.RNum = 1
Idea is to assign distinct row number inside group PID and then get the one with RowNumber = 1
For SQl Server 2000
Select Distinct First_Name,Last_Name,P_ID
From Table1 T1
INNER JOIN
(
Select Min(First_Name) First_Name,P_ID
From Table1 T1
Group By P_ID
) T2 ON T1.P_ID = T2.P_ID AND T1.First_Name = T2.First_Name
Note: In case when two rows have same P_ID and First_Name and Different Last_Name it will return 2 rows. I am checking for that.
Another is way to create a temp table with Identity Column. Then instead of using min(First_Name) in inner query we will use min(Idenity) group by P_ID and in join we will use P_ID and identity for join.