Is Group Multiplication Possible in Non-Mathematical Topics?

[physics1000]

TL;DR

Okay, what I mean:
Lets say I have the group $\mathbb{N}$
If I have a vector product of A x B which has a, 3a
Can I write Dom(R) as $\mathbb{N}$ and Range(R) as $\mathbb{N} * 3$?

Sorry if it didnt belong.
its not at calculus or linear algebra.

 

[PeroK]

$\mathbb N$ is not a group. Do you mean set?

Use double dollars or double hashes to fix your Latex.

 

[fresh_42]

This question is a mess. $\mathbb{N}$ is no group, to begin with. Then your product $A\times B$ doesn't look like a vector product. It's probably a direct product.

If you have groups, you can build semidirect, or direct products. Also, tensor products are possible in certain cases.

 

[mfb]

Are you asking if you can write $\{3a, a \in \mathbb{N}\}$ as $\mathbb{N}\cdot 3$? It looks awkward but its possible to understand what you mean.

 

[Mark44]

Use double dollars or double hashes to fix your Latex.

Fixed...

 

[WWGD]

You can describe the output as $\{(a,3a)\}$.

 

[physics1000]

Thanks guys for the answers.
Sorry for my bad latex... ( and bad english )