Question

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.

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 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.
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.
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
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)
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 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 p be an prime. Use the action of G = GL2(Z/pZ) on (Z/pZ)2 and the...
Let p be an prime. Use the action of G = GL2(Z/pZ) on (Z/pZ)2 and the orbit-stabilizer theorem to compute the order of G (Given an element x ∈ X, the orbit O(x) of x is the subsetO(x)={g·x: g∈G}⊂X. Here, we write g · x for ρ(g)(x). The stabilizer of x ∈ X is the subset Gx ={g∈G: g·x=x}⊂G. This is a subgroup of G, and the orbit-stabilizer theorem says (in a particular form) that if G is a finite...
: (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...
Let p be a prime and m an integer. Suppose that the polynomial f(x) = x^4+mx+p...
Let p be a prime and m an integer. Suppose that the polynomial f(x) = x^4+mx+p is reducible over Q. Show that if f(x) has no zeros in Q, then p = 3.
Let p,q be prime numbers, not necessarily distinct. If a group G has order pq, prove...
Let p,q be prime numbers, not necessarily distinct. If a group G has order pq, prove that any proper subgroup (meaning a subgroup not equal to G itself) must be cyclic. Hint: what are the possible sizes of the subgroups?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT