Question

Please help! Give an example which shows that the union of subgroups is not a subgroup in general.

Answer 1

Take the set of integers with the operation addition. This is a group.

Now look at all the multiples of 3. This is a subgroup. Also look at the multiples of 5, another subgroup. The union of these 2 subgroups is the set of all multiples of 3 and 5, but it is not a subgroup, because if you add any multiple of 3 and any multiple of 5, you dont always get a multiple of 3 or 5 (for example, 3+5=8, which is not a multiple of 3 or 5).

Answer 2

Thank you!