I am having trouble understanding this example:(adsbygoogle = window.adsbygoogle || []).push({});

Let G=S_3 and H={(1),(13)}. Then the left cosets of H in G are

(1)H=H

(12)H={(12), (12)(13)}={(12),(132)}=(132)H

I cannot figure out how to produce this relation:

(12)H={(12), (12)(13)}={(12),(132)}=(132)H

I understand (12)H={(12), (12)(13)} but not how (12)(13) = (132) or the equivalence after that...

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

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 of a subset of S_3

Loading...

Similar Threads - Cosets subset | Date |
---|---|

A Lagrange theorems and Cosets | Dec 16, 2017 |

I Multiplicative cosets | May 4, 2017 |

I For groups, showing that a subset is closed under operation | Feb 20, 2017 |

I Question about coset | Apr 20, 2016 |

I Why only normal subgroup is used to obtain group quotient | Mar 5, 2016 |

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