Question

True or False? The union of 2 subgroup is a subgroup.

I think is false any 1 got explaination for it or think it should be true?

Answer 1

i think it is true because the union of two subgroups forms one new subgroup.

Answer 2

it makes logical sense but i have no idea what kind of subgroups you are talking about

Answer 3

It's false. Consider this example:

Let (Z,+) be a group of all integers under normal addition.
Then, (Z(2),+) is a subgroup, where Z(2) is all integers that are a multiple of two.
Similarly, (Z(3),+) is a subgroup, where Z(3) is all integers that are a multiple of three.
Define S = Z(2) U Z(3)

Now, pick two elements in S, say 2 and 3. 2 + 3 = 5, which is not in Z(2) or Z(3). So, S is not closed under +. It's not a subgroup.

Answer 4

Thanks for yout example