Question

16. Let
G be a finite group . Let
H and K be subgroup of G
such that
H is a subgroup of k

then
​

Answer 1

Answer:

I love you boys........

Answer 2

Step-by-step explanation:

let G be a group and let H, K be two subgroups of G such that H ∪K

is also a subgroup. Prove that either H ⊆ K or K ⊆ H.

Solution: Suppose that neither H ⊆ K nor K ⊆ H. Then there is h ∈ H,

h 6∈ K and there is k ∈ K, k 6∈ H. Since H ∪ K is a subgroup, we have hk ∈ H ∪ K.

It follows that hk ∈ H or hk ∈ K. In the former case, k = h

−1

(hk) ∈ H and the

latter case h = (hk)k

−1 ∈ K. In both cases we get a contradiction.

mark as brilliant and take thanks for all question and follow