Galois and Klein 4: Isomorphic or Cyclic?

Level: Graduate
Thread starter morganjp
Start date Dec 12, 2007
Tags

Klein

Join the discussion

Registration is free. Start your own thread to ask a follow-up.

1 reply · 2K views

morganjp

Thread starter
Dec 12, 2007

suppose a +ve degree polynomial g(x) in G[x] with F splits over G and no irr. factor has repeated root. then if [F:G]=4, we know the size of Gal(F/G) is also 4. so it's either isomorphic to the Klein 4 or cyclic group of order 4. is there any trick to tell it's one and not the other?

Physics news on Phys.org

Ultrathin materials could make quantum light circuits programmable
Spin rephasing helps quantum memories store single-photon states longer for future networks
Discovery confirms rare, switchable electrical property in widely used electronics material

Discussion

morphism

Science Advisor

Homework Helper

Dec 12, 2007

The Galois group will permute the roots. Can you find a permutation of order 4?

Galois and Klein 4: Isomorphic or Cyclic?

Discussion

Similar threads

Graduate How are R^2 and R^4 isomorphic as VS's over Q?

Proof: Proving Klein 4 Group is Not Isomorphic to ##Z_4##

Are All Groups of Order 4 Isomorphic to Z/4Z or the Klein Group?

Graduate Galois group isomorphic to quaternions implies degree at least 8?

Graduate Showing the Galois group of Q(⁴√2, i) over Q is isomorphic to D4

Finding splitting field and Galois group questions

Galois group and fixed fields of x^3 + 4 over Q

Graduate Galois Theory (degree 4 polynomial)

Graduate Minimal polynomial and Galois group of √3 + √7

When is G isomorphic to a Galois group of degree d?