How are non-associative groups called?

Question

Is there a name for the algebraic objects that have all the properties of groups except associativity?

For example, the unit octonions have this property. They satisfy the following definition.

Definition: A set $G$ is called a _________ if there is a binary operation $\cdot:G\times G\to G$ such that

1. (Identity) There exists an element $e\in G$, such that $e \cdot a = a \cdot e = a$ for all $a\in G$.
2. (Inverse) For all $a \in G$, there exists an element $b \in G$ such that $a \cdot b = b \cdot a = e$.