Question

(a) Show that H =<(1234)> is a normal subgroup of G=S4 (b) Is the quotient group...

(a) Show that H =<(1234)> is a normal subgroup of G=S4

(b) Is the quotient group G/H abelian? Justify?

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 H be a normal subgroup of G. Assume the quotient group G/H is abelian. Prove...
Let H be a normal subgroup of G. Assume the quotient group G/H is abelian. Prove that, for any two elements x, y ∈ G, we have x^ (-1) y ^(-1)xy ∈ H
Show that if G is a group, H a subgroup of G with |H| = n,...
Show that if G is a group, H a subgroup of G with |H| = n, and H is the only subgroup of G of order n, then H is a normal subgroup of G. Hint: Show that aHa-1 is a subgroup of G and is isomorphic to H for every a ∈ G.
Let G be a finite group, and suppose that H is normal subgroup of G. Show...
Let G be a finite group, and suppose that H is normal subgroup of G. Show that, for every g ∈ G, the order of gH in G/H must divide the order of g in G. What is the order of the coset [4]42 + 〈[6]42〉 in Z42/〈[6]42〉? Find an example to show that the order of gH in G/H does not always determine the order of g in G. That is, find an example of a group G, and...
Suppose that H is a normal subgroup of G and K is any subgroup of G....
Suppose that H is a normal subgroup of G and K is any subgroup of G. Define HK = {hk : h ? H, k ? K}. (a) Show that HK is a subgroup of G. (b) Does the conclusion of (a) continue to hold if H is not normal in G? Justify
Let G be an Abelian group and H a subgroup of G. Prove that G/H is...
Let G be an Abelian group and H a subgroup of G. Prove that G/H is Abelian.
A subgroup H of a group G is called a normal subgroup if gH=Hg for all...
A subgroup H of a group G is called a normal subgroup if gH=Hg for all g ∈ G. Every Group contains at least two normal subgroups: the subgroup consisting of the identity element only {e}; and the entire group G. If G=S(n) show that A(n) (the subgroup of even permuations) is also a normal subgroup of G.
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 .
In each part below, a group G and a subgroup H are given. Determine whether H...
In each part below, a group G and a subgroup H are given. Determine whether H is normal in G. If it is, list the elements of the quotient group G/H. (a) G = Z-15 × Z-20 and H = <(10, 17)> (b) G = S-6 and H = A-6 (c) G = S-5 and H = A-4
(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.
Suppose : phi :G -H is a group isomorphism . If N is a normal subgroup...
Suppose : phi :G -H is a group isomorphism . If N is a normal subgroup of G then phi(N) is a normal subgroup of H. Prove it is a subgroup and prove it is normal?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT