# Multiply a Group - possible?

• I
• physics1000
In summary, the conversation discusses the use of double dollars or double hashes to fix Latex and the possibility of writing ##\{3a, a \in \mathbb{N}\}## as ##\mathbb{N}\cdot 3##. It is also mentioned that ##\mathbb{N}## is not a group and that the product ##A\times B## is likely a direct product. Additionally, the conversation mentions the possibility of building semidirect or direct products with groups and the possibility of tensor products in certain cases.

#### physics1000

TL;DR Summary
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.

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

Use double dollars or double hashes to fix your Latex.

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.

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.

PeroK said:
Use double dollars or double hashes to fix your Latex.
Fixed...

jim mcnamara
You can describe the output as ##\{(a,3a)\}##.