Assignment:  

(1)  Use the subgroup { I, (12) } to partition S3.

     |------------|
     | (23) (123) | (23) 
     |------------|
     | (13) (132) | (13)
     |------------|
     |  I, (12)   |
     |------------|

(2)  Use the subgroup  5 Z = {...-10,-5,0,5,10,15 ....} 

to partition Z.

      |---------------------------|
      |                           |
      | ..., -6,-1,4,9,14,19,...  |
      |                           |
      |---------------------------|
      |                           |
      | ..., -7,-2,3,8,13,18,...  |
      |                           |
      |---------------------------|
      |                           |
      | ..., -8,-3,2,7,12,17,...  |
      |                           |
      |---------------------------|
      |                           |
      | ..., -9,-4,1,6,11,16,...  |
      |                           |
      |---------------------------|
      |                           |
      | ...,-10,-5,0,5,10,15,...  |
      |                           |
      |---------------------------|





(3) Use the Kleinfour group to partition A4.


     |-------------------------------------|
     |                                     |
     | (132)  (143)    (234)      (124)    |  (132) 
     |                                     |
     |-------------------------------------|
     |                                     |
     | (123)  (243)    (142)      (134)    |  (123)
     |                                     |
     |-------------------------------------|
     |                                     |
     |   I  (12)(34)   (13)(24)   (14)(23) |
     |                                     |
     |-------------------------------------|

(4) Use the Kleinfour group to partition S4.



     |-------------------------------------|
     |                                     |
     |  (23)   (1243)   (1342)    (14)     |   (23)
     |                                     |
     |-------------------------------------|
     |                                     |
     |  (13)   (1432)   (24)      (1234)   |   (13)
     |                                     |
     |-------------------------------------|
     |                                     |
     |  (12)   (34)    (1423)     (1324)   |   (12)
     |                                     |
     |-------------------------------------|
     |                                     |
     | (132)  (143)    (234)      (124)    |  (132) 
     |                                     |
     |-------------------------------------|
     |                                     |
     | (123)  (243)    (142)      (134)    |  (123)
     |                                     |
     |-------------------------------------|
     |                                     |
     |   I  (12)(34)   (13)(24)   (14)(23) |
     |                                     |
     |-------------------------------------|