Question

Let G and G′ be two isomorphic groups that have a unique normal subgroup of a...

Let G and G′ be two isomorphic groups that have a unique normal subgroup of a given
order n, H and H′. Show that the quotient groups G/H and G′/H′ are isomorphic.
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 G1 and G2 be isomorphic groups. Prove that if G1 has a subgroup of order...
Let G1 and G2 be isomorphic groups. Prove that if G1 has a subgroup of order n, then G2 has a subgroup of order n
Let N be a normal subgroup of G. Show that the order 2 element in N...
Let N be a normal subgroup of G. Show that the order 2 element in N is in the center of G if N and Z_4 are isomorphic.
Let H be a subgroup of G, and N be the normalizer of H in G...
Let H be a subgroup of G, and N be the normalizer of H in G and C be the centralizer of H in G. Prove that C is normal in N and the group N/C is isomorphic to a subgroup of Aut(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 let H be a subgroup of order n. Suppose...
Let G be a finite group and let H be a subgroup of order n. Suppose that H is the only subgroup of order n. Show that H is normal in G. Hint: Consider the subgroup aHa-1 of G. Please explain in detail!
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
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...
Let G and H be groups, and let G0 = {(g, 1) : g ∈ G}...
Let G and H be groups, and let G0 = {(g, 1) : g ∈ G} . (a) Show that G0 ≅ G. (b) Show that G0 is a normal subgroup of G × H. (c) Show that (G × H)/G0 ≅ H.
Let G and H be groups and f:G--->H be a surjective homomorphism. Let J be a...
Let G and H be groups and f:G--->H be a surjective homomorphism. Let J be a subgroup of H and define f^-1(J) ={x is an element of G| f(x) is an element of J} a. Show ker(f)⊂f^-1(J) and ker(f) is a normal subgroup of f^-1(J) b. Let p: f^-1(J) --> J be defined by p(x) = f(x). Show p is a surjective homomorphism c. Show the set kef(f) and ker(p) are equal d. Show J is isomorphic to f^-1(J)/ker(f)
Determine if the indicated subgroup H is a normal subgroup of G. (a) Let G =...
Determine if the indicated subgroup H is a normal subgroup of G. (a) Let G = Z and H = 6Z. (b) Let G = A4 and H = {id,(12)(34),(13)(24),(14)(23)}.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT