Find all possible orders of elements in the group Z4 × Z5 × Z10.
For each possible order, give an example of an element of that
order, and prove that no other orders are possible.
If possible, find
A + B, A −
B, 2A, and 2A
− 5B.
(If not possible, enter IMPOSSIBLE.)
A =
3
−1
1
2
4
3
, B =
−1
1
−5
−4
3
−2
(a) A + B
(b) A − B
(c) 2A
(d) 2A − 5B