Greetings,(adsbygoogle = window.adsbygoogle || []).push({});

For a homomorphism [itex]\varphi[/itex], I'm trying to show that elements of a fiber, say the fiber above [itex]a[/itex], [itex]X_a[/itex], are writable as a given element of [itex]X_a[/itex] times an element of the kernel [itex]K[/itex]. So, if [itex]a\in X_a[/itex] and [itex]b\in X_a[/itex], then [itex]\exists k\in K[/itex] such that [itex]b=ak[/itex].

I want to do this without using the theorem that [itex]\{[/itex]left cosets of [itex]K[/itex] in [itex]G\} =G/K[/itex] - in fact, one of my motivations for looking for this is that I want a different proof of this theorem then the ones that I have seen.

Does anyone know of a way to do this?

Thanks for any help that you can give.

-HJ Farnsworth

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

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

# Abstract algebra: elements of fiber writable as

Loading...

Similar Threads - Abstract algebra elements | Date |
---|---|

I What are the groups for NxNxN puzzle cubes called? | Dec 24, 2017 |

I Free Groups | Oct 19, 2017 |

Another question from Elements of Abstract Algebra by Clark - transformation groups | Jul 6, 2006 |

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