HW, 3rd exercise

Greetings, about the third exercise, I have to make a comment here, if I’m not mistaken, we need to choose x\neq 0 because 0 also have the property that \Delta(0)=0\otimes0 but it doesn’t belong to the group.
I think that could help. (Thanks to Yiby Morales, she encouraged me to post this!)



  1. Brian Cruz

    Thanks Sebastian (and thanks Yiby)!

    I was thinking the same thing and came to the forum to see if anyone had posted about it! I think you’re right, and the PlanetMath website seems to say the same thing about the grouplike element.


  2. alyssapalfreyman

    In the group ring is it appropriate to consider the elements of $latexG$ as a basis for $latex\mathbb{F}[G]$ and therefore the pure tensors of elements of $latexG$ as a basis for $latex\mathbb{F}[G]\otimes\mathbb{F}[G]$? My hope is that two elements of $latex\mathbb{F}[G]\otimes\mathbb{F}[G]$ are equal only if the coefficients of corresponding pure tensors are equal. Is this true?

  3. alyssapalfreyman

    also, how do you get the latex to compile?

  4. Sebastián O.

    alyssapalfreyman, the basis of the \mathbb{F}[G] \otimes \mathbb{F}[G] are exactly the elements g \otimes g' with g, g' \in G

    PD: You write $, then latex, spacebar, then the latex code, and last you close with $.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: