Given that ϕ is a isomorphism from a group G under addition to a group G under addition, convert property 2 of Theorem 6.2 to additive notation.

To convert property 2 of Theorem 6.2 into additive notation, we first need to recall what property 2 of Theorem 6.2 states in the context of group theory. This property generally pertains to the behavior of isomorphisms between groups, particularly regarding the preservation of group operations.

Understanding Theorem 6.2 Context

In the context of an isomorphism $\phi: G \to H$ between two groups $G$ and $H$:

1. $\phi$ is a bijective function.
2. The property typically asserts that the operation is preserved, namely:

$\phi(a * b) = \phi(a) * \phi(b)$

for all $a, b \in G$.

Conversion to Additive Notation

In the case of groups under addition, we can represent the group operation with the symbol $+$. Therefore, property 2 in additive notation would become:

$\phi(a + b) = \phi(a) + \phi(b)$

for all $a, b \in G$.

Final Answer

In additive notation, property 2 of Theorem 6.2 can be expressed as:

$\phi(a + b) = \phi(a) + \phi(b) \quad \forall a, b \in G$