Question

(a) Show that A ⊆ NG(A) is not necessarily true when A is not a subgroup...

(a) Show that A ⊆ NG(A) is not necessarily true when A is not a subgroup of G, but just a subset.

(b) Let H be a subgroup of order 2 in G. Show that NG(H) = CG(H).

(c) Show that H ≤ CG(H) if and only if H is abelian.

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
(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?
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 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 be a finite Abelian group and let n be a positive divisor of|G|. Show...
Let G be a finite Abelian group and let n be a positive divisor of|G|. Show that G has a subgroup of order n.
Let G be a non-abelian group of order p^3 with p prime. (a) Show that |Z(G)|...
Let G be a non-abelian group of order p^3 with p prime. (a) Show that |Z(G)| = p. (b) Suppose a /∈ Z(G). Show that |NG(a)| = p^2 . (c) Show that G has exactly p 2 +p−1 conjugacy classes (don’t forget to count the classes of the elements of Z(G)).
Prove that if A is a subgroup of G and B is a subgroup of H,...
Prove that if A is a subgroup of G and B is a subgroup of H, then the direct product A × B is a subgroup of G × H. Show all steps. Note that AXB is nonempty since the identity e is a part of A X B. Remains only to show that A X B is closed under multiplication and inverses.
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 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.
1) Let G be a group and N be a normal subgroup. Show that if G...
1) Let G be a group and N be a normal subgroup. Show that if G is cyclic, then G/N is cyclic. Is the converse true? 2) What are the zero divisors of Z6?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT