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

I'm taking a math course at university that covers introductory group theory. The textbook's definition of the identity element of a group defines it as two sided; that is, they say that a group ##G## must have an element ##e## such that for all ##a \in G##, ##e \cdot a = a = a \cdot e## .

Is it possible to define a group's identity element as one-sided, and then prove two-sidedness as a theorem? Or is it an intrinsic property of group identities?

I started with a left-identity ##e \cdot a = a## and tried to prove that ##e \cdot a = a = a \cdot e## and kept hitting walls, so I though I'd better check if it's doable.

Thanks.

**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!

# Identity Element in Groups

Loading...

Similar Threads for Identity Element Groups |
---|

I Question about groups |

I Spin group SU(2) and SO(3) |

I What is difference between transformations and automorphisms |

I Lorentz group representations |

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