What Group Contains Elements a and b in Abstract Algebra?

[ShengyaoLiang]

1)
find a group that contains elements a and b such that ︱a︱=︱b︱= 2 and

a) ︱ab︱ = 3 b) ︱ab︱=4 c) ︱ab︱=5

2)
suppose that H is a proper subgroup of Z under addition and H contains 18, 30 and 40.
determine H?


does anyone can help me out?
and ...i am really in hurry...thanks...

besides...i need all the steps...

 

[ShengyaoLiang]

can somebody help me out?

especially the second question...

 

[Hurkyl]

What have you tried? Have you had any thoughts at all on these problems?