Let the set G- ZX Z and the binary operation on G be given by the rule (a, b) • (c, d) commutative group. = (a + r, 6+ d). It is easily verified that the pair (G, ) is a - a is a homomorphism a) Show that the mapping f: G-Z defined by fl(a, b)] from (G, ) onto the group (Z,+). b) Determine the kernel of this mapping. c) If II = {(a, a) | a E Z}, prove that (H,) is a subgroup of (G, ), which is isomorphic to (Z,+) under the function f. %3D

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