The group of integers under addition has the identity element:a.-1b.0c.1d.∞

To determine the identity element of the group of integers under addition, we need to find an element that, when added to any other integer, does not change its value.

Let's consider each option:

a. -1: If we add -1 to any integer, the result will be one less than the original integer. Therefore, -1 is not the identity element.

b. 0: Adding 0 to any integer does not change its value. So, 0 is the identity element.

c. 1: Adding 1 to any integer will result in one more than the original integer. Thus, 1 is not the identity element.

d. ∞ (infinity): Infinity is not a valid integer, so it cannot be the identity element.

Therefore, the correct answer is b. 0.