Homomorphism 6

If G is a group and N is a normal subgroup of G, show that if a in G has finite order o(a), then Na in G/N has finite order m, where m|o(a). (Prove this by using the homomorphism of G onto G/N.)

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Originally Posted by mpryal

If G is a group and N is a normal subgroup of G, show that if a in G has finite order o(a), then Na in G/N has finite order m, where m|o(a). (Prove this by using the homomorphism of G onto G/N.)

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Let be the natural projection homomorphism i.e. .
Let then order of must divide order of by the properties of homomorphism.
Thus, we see that .