Question

(Abstract algebra) Let G be a group and let H and K be subgroups of G...

(Abstract algebra) Let G be a group and let H and K be subgroups of G so that H is not contained in K and K is not contained in H. Prove that H ∪ K is not a subgroup of G.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let G be a group with subgroups H and K. (a) Prove that H ∩ K...
Let G be a group with subgroups H and K. (a) Prove that H ∩ K must be a subgroup of G. (b) Give an example to show that H ∪ K is not necessarily a subgroup of G. Note: Your answer to part (a) should be a general proof that the set H ∩ K is closed under the operation of G, includes the identity element of G, and contains the inverse in G of each of its elements,...
(a) Prove or disprove: Let H and K be two normal subgroups of a group G....
(a) Prove or disprove: Let H and K be two normal subgroups of a group G. Then the subgroup H ∩ K is normal in G. (b) Prove or disprove: D4 is normal in S4.
Let H and K be subgroups of a group G so that HK is also a...
Let H and K be subgroups of a group G so that HK is also a subgroup. Show that HK = KH.
Let H and K be subgroups of G. Prove that H ∪ K is a subgroup...
Let H and K be subgroups of G. Prove that H ∪ K is a subgroup of G iff H ⊆ K or K ⊆ H.
f H and K are subgroups of a group G, let (H,K) be the subgroup of...
f H and K are subgroups of a group G, let (H,K) be the subgroup of G generated by the elements {hkh−1k−1∣h∈H, k∈K}. Show that : H◃G if and only if (H,G)<H
Let G be a finite group and let H, K be normal subgroups of G. If...
Let G be a finite group and let H, K be normal subgroups of G. If [G : H] = p and [G : K] = q where p and q are distinct primes, prove that pq divides [G : H ∩ K].
(a) Prove or disprove: if H and K are subgroups of G, then H ∩ K...
(a) Prove or disprove: if H and K are subgroups of G, then H ∩ K is a subgroup of G. (b) Prove or disprove: if H is an abelian subgroup of G, then G is abelian
Suppose that G is a group with subgroups K ≤ H ≤ G. Suppose that K...
Suppose that G is a group with subgroups K ≤ H ≤ G. Suppose that K is normal in G. Let G act on G/H, the set of left cosets of H, by left multiplication. Prove that if k ∈ K, then left multiplication of G/H by k is the identity permutation on G/H.
Let G be an Abelian group and let H be a subgroup of G Define K...
Let G be an Abelian group and let H be a subgroup of G Define K = { g∈ G | g3 ∈ H }. Prove that K is a subgroup of G .
If H and K are arbitrary subgroups of G. Prove that HK is a subgroup of...
If H and K are arbitrary subgroups of G. Prove that HK is a subgroup of G if and only if HK=KH.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT