Let H={sigma in S_5 | sigma94)=4} Show that H<=S_5

Aneeka Hunt 2021-01-31 Answered
Let H={σS5σ94)=4}
Show that HS5
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Roosevelt Houghton
Answered 2021-02-01 Author has 106 answers

σ is bijective map from {1,2,3,4,5}{1,2,3,4,5}
but σ(4)=4
σ is bijective map from {1,2,3,4,5}{1,2,3,4,5}
If f,gH
fg1(4)=f(g1(4))=f(4)=4
fg1(4)=4
fg1H

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-11-20
Prove that in any group, an element and its inverse have the same order.
asked 2021-12-30
Let F be a field. Suppose that a polynomial p(x)=a0+a1x++anxn is reducible in F[x]. Prove that the polynomial q(x)==xnp(1x)=an+an1x+a0xn is also reducible.
asked 2022-01-14
Consider Fp, the algebraic closure of Fp. I want to see that: for every proper subfield KFp,FpK is not a finite extension.
It is known that, and can be somewhat easily shown that Fp=n1Fpn.
Now, if any of the proper subfields have the form Fpn, it is easy enough to see that FpFpn(α1,,αm) for some αi by going high up enough, i.e, to some big enough m such that αiFpmFp
The problem is characterizing the proper subfields. Is every subfield of Fp going to have this form? Can we have an infinite intermediate subfield?
asked 2022-04-14
Let G be a finite group. Let T be an element of Aut(G) such that
T2=I, and xT=xx=e.
Then, G is abelian.
asked 2021-09-21

Let f1,…,fr be complex polynomials in the variables x1,…,xn let V be the variety of their common zeros, and let I be the ideal of the polynomial ring R=C[x1,…,xn] that they generate. Define a homomorphism from the quotient ring R=R/I. I to the ring R of continuous, complex-valued functions on V.

asked 2022-05-02
Prove that Z+(3x) is a subring of Z[x] and there is no surjective homomorphism from Z[x]Z+(3x)
asked 2022-02-12
Determine order of 123452354.
I'm asked to prove that the order of H=123452354 is 20, in an Algebra exercise 2nd year maths.
What I have achieved is that 20||H|and|H=20,120 since H can't be the alternating group and there are no subgroups of order 40 in S5. But I don't know how to prove HS5.

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question