# Properties of grouping in relational algebra

The properties of relational algebra (commutativity, associativity, distribution) allow us to take a relational algebra expression and transform/rewrite it into another one which is logically equivalent. However, I am struggling to find any such properties as far as the grouping operator Ɣ is concerned.

I am not sure but I think Ɣ is derived from the other relational operators? Is this correct? I would suppose that if this is correct, then it explains why it is harder to find such properties. That being said, Ɣ (GROUP BY) remains a very important operator, so how can one reason about its properties in relational algebra? Has this been done before?

• The group by operator cannot be derived by others, in fact it is considered an extension of the classical relational algebra. There are properties that can be proved to transform an expression with it in another expression with or without a group by, but with complex conditions over the operands. – Renzo Feb 14 at 4:42
• So are there any properties of this group by operator as it relates to the classical relational operators? – Zeruno Feb 15 at 11:42
• Am I correct to understand that we can transform an expression with the group by operator into one with a classical relational operator? Can we always do this? – Zeruno Feb 17 at 11:29