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

I have a small question about groups,

If you have a comunitative 'group' H = <a in H : a^{2}=1>,

Is that enough information to show that it is a group, without knowing the binary operation?

say b is also in H

then a*b=b*a

(a*b)*(b*a) = (a*a)*(b*b) = 1 (since its comunitative)

So that shows there is an identity, and each element is it's own inverse

It's also associative so everything is satisfied for H to be a group,

So only knowing these two properties of this group can show that it is indeed a group?

**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!

# Comunitative Group

Loading...

Similar Threads for Comunitative Group | Date |
---|---|

I Spin group SU(2) and SO(3) | Apr 5, 2018 |

I What is difference between transformations and automorphisms | Mar 30, 2018 |

I Lorentz group representations | Mar 28, 2018 |

I Correspondence Theorem for Groups ... Another Question ... | Mar 24, 2018 |

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