(G is a group, and H is a subgroup of G). I've just read in a book, that all distinct (left or right) cosets of H in G form a partition of G, i.e. that G is equal to the union of all those cosets. Apparently, this follows from the fact that two cosets are either equal or disjoint (I've proved that), but I just can't figure out how the whole partition thing follows. It must be either very hard or very easy to prove, as it is stated without proof in the book... Can anyone shed some light on this?(adsbygoogle = window.adsbygoogle || []).push({});

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

Dismiss Notice

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!

# Cosets are either equal or disjoint

Loading...

Similar Threads for Cosets either equal |
---|

A Lagrange theorems and Cosets |

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