Hi, I'm looking at proposition 1.14(c) of Artin's Algebra.(adsbygoogle = window.adsbygoogle || []).push({});

It says

if we have K a splitting field for polynomial f from F[x], with roots a_1,...,a_n,

then the Galois group G(K/F) acts faithfully on the set of roots.

I look at faithful as the symmetries in the roots completely represent the group.

That is, no root is fixed by any group element (besides the identity (edited)).

When should I worry about this, are there any ways to construct a relevant counterexample if we drop a condition?

(So for actions, transitive and faithful is like surjectivity and injectivity respectively?)

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# When is a Galois group not faithful

Loading...

Similar Threads - Galois group faithful | Date |
---|---|

B Galois Groups ... A&F Example 47.7 ... ... | Jul 7, 2017 |

I Galois Groups ... A&W Theorem 47.1 ... ... | Jul 4, 2017 |

Book for abstract algebra (group and galois theory) | Apr 19, 2015 |

Galois Theory, Differential Equations, and Lie Groups? | Jun 6, 2014 |

Galois Groups of Extensions by Roots of Unity | Apr 24, 2012 |

**Physics Forums - The Fusion of Science and Community**