Lazard-divided associative operad

Definition
The Lazard-divided Lie operad is an operad over $$\mathbb{Z}$$ that is intermediate between the associative operad over $$\mathbb{Z}$$ and the associative operad over $$\mathbb{Q}$$. It is defined as follows: consider the Lie operad over $$\mathbb{Q}$$, and take the $$\mathbb{Z}$$-suboperad generated by the following operations, one for each prime number $$p$$:

$$(x_1,x_2,\dots,x_p) \mapsto \frac{1}{p}(x_1x_2 \dots x_p)$$

Related notions

 * Lazard-divided Lie operad