Define what a quotient group is both as a set and its compos

Define what a quotient group is: both as a set and its composition law. Ls Q isomorphic to Z times (Q/Z)?

Solution

a) A quotient group H of a group G is the set defined as

H ={x+a | x€G and a€A where A is a normal subgroup of G}

According to its composition it is given as H=G/A where A is the normal subgroup of G and H has the elements of the type x+a where x is an elememt of the group G and a is the element of the normal subgroup A