# Defining an abstract multiplication over finite indices

I would like to define a map (a "multiplication" denoted $\otimes$) over the finite set of symbols $G=\{a,b,c,d,e,f,g,h\}$. I would like to define several rules like $$a \otimes b= \{b \}$$ $$a \otimes h= \{h,g\}$$

etc. So the mapping is from $G \times G$ to the power set of G (i.e, to the set of all subsets of G). Can someone kindly suggest some ways as to define such an abstract system of labels, and the above map?

• a\[TensorProduct]h = {h, g}? – AccidentalFourierTransform Jul 7 '18 at 14:53
• @AccidentalFourierTransform Yes. Tensor product is just a symbol that I am using for the map $\otimes: G \times G \rightarrow P(G)$ where P(G) denotes the power set of G. – Rajath Krishna R Jul 7 '18 at 14:55