Question

Suppose N is a normal subgroup of G such that |G/N|= p is a prime. Let...

Suppose N is a normal subgroup of G such that |G/N|= p is a prime. Let K be any subgroup of G. Show that either (a) K is a subgroup of N or (b) both G=KN and |K/(K intersect N)| = p.

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
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 p be a prime. Show that a group of order pa has a normal subgroup...
Let p be a prime. Show that a group of order pa has a normal subgroup of order pb for every nonnegative integer b ≤ a.
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 let P be a Sylow p-subgroup of G. Suppose...
Let G be a finite group and let P be a Sylow p-subgroup of G. Suppose H is a normal subgroup of G. Prove that HP/H is a Sylow p-subgroup of G/H and that H ∩ P is a Sylow p-subgroup of H. Hint: Use the Second Isomorphism theorem.
Let P be a subgroup of Sn of prime order, and suppose the element x in...
Let P be a subgroup of Sn of prime order, and suppose the element x in Sn normalizes but does not centralize P. Show that x fixes at most one point in each orbit of P. Help with a solution would be appreciated.
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.
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?
Let G be a group of order p^2, where p is a prime. Show that G...
Let G be a group of order p^2, where p is a prime. Show that G must have a subgroup of order p. please show with notation if possible
: (a) Let p be a prime, and let G be a finite Abelian group. Show...
: (a) Let p be a prime, and let G be a finite Abelian group. Show that Gp = {x ∈ G | |x| is a power of p} is a subgroup of G. (For the identity, remember that 1 = p 0 is a power of p.) (b) Let p1, . . . , pn be pair-wise distinct primes, and let G be an Abelian group. Show that Gp1 , . . . , Gpn form direct sum in...
If G is a group of order (p^k)s where p is a prime number such that...
If G is a group of order (p^k)s where p is a prime number such that (p,s)=1, then show that each subgroup of order p^i ; i= 1,2...(k-1) is a normal subgroup of atleast one subgroup of order p^(i+1)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT