8. (a) Let G b e the group Z2 ⊕ Z2. Show that G is not y li . [5 marks℄(b) Let G b e the group Z3 ⊕ Z2. Show that G is y li . [4 marks℄

The question seems to be about group theory in mathematics, specifically about cyclic groups. However, the question is not clear due to some missing information and typographical errors.

In general, to show whether a group is cyclic or not, you need to determine if there is a single element (generator) in the group that can generate all other elements of the group through its powers.

(a) The group Z2 ⊕ Z2 is not cyclic. This is because it does not have a single generator. The group Z2 ⊕ Z2 has four elements: (0,0), (0,1), (1,0), and (1,1). No single element can generate all other elements through its powers.

(b) The group Z3 ⊕ Z2, on the other hand, is cyclic. This is because it has a single generator. The group Z3 ⊕ Z2 has six elements: (0,0), (0,1), (1,0), (1,1), (2,0), and (2,1). The element (1,1) can generate all other elements through its powers, making the group cyclic.

Please note that this is a general explanation and the specifics might vary based on the exact definitions and properties of the groups in your course.