The definition given is...(adsbygoogle = window.adsbygoogle || []).push({});

"Let ##\phi: G \rightarrow H## be a homomorphism with kernel ##K##. The quotient group ##G/K## is the group whose elements are the fibers (sets of elements projecting to single elements of H) with group operation defined above: namely if ##X## is the fiber above ##a## and ##Y## is the fiber above b then the product of ##X## and ##Y## is defined to be the fiber above the product ##ab##."

But what if we have a homomorphism ##\alpha: G \rightarrow A## and a homomorphism ##\beta: G \rightarrow B## that both have kernel ##K##?

Wouldn't this mean ##G/K## is not unique because ##\alpha: G \rightarrow A## requires ##G/K## to be fibers consisting of elements in ##A## whereas ##\beta: G \rightarrow B## requires ##G/K## to be fibers consiting of elements in ##B##?

I'm confused. :(

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Help Understanding Quotient Groups? (Dummit and Foote)

Loading...

Similar Threads for Help Understanding Quotient |
---|

I Understand homomorphisms from Z^a --> Z^b |

I Quotient Rings ... Remarks by Adkins and Weintraub ... |

I Understanding Hilbert Vector Spaces |

B Help understanding a proof |

**Physics Forums | Science Articles, Homework Help, Discussion**