[R] manipulate group data using column name

[sun]

Hi,

 Maybe this is a trivial question but I can not figure out a good solution.

I have a data frame fa and want to add a new column "sum" with the sum value 
of fa$X1 grouped by fa$X3.

> fa
   X1 X2 X3
1   1 11  1
2   2 12  1
3   3 13  1
4   4 14  2
5   5 15  2
6   6 16  2
7   7 17  3
8   8 18  3
9   9 19  3
10 10 20  3

fa$X3 is the index of group

i can

>aggregate(fa[,"X1"],list(fa$X3),sum)
  Group.1  x
1       1  6
2       2 15
3       3 34

then I want to add a new column "sum" in fa and assign the aggregated result 
to the new column. Is there a solution without using loops?
or maybe there is some way can even avoid aggregate operation?

Thanks.