Remark

The fact that B is a generating set of G means that each element of G can be written as a product of elements from B and their inverses.

Since G is finite, however, we do not need the inverses, for, if b B, then <b> is finite, so there is a positive integer n with bⁿ = e. But then b^-1 = b^n-1, so indeed, the inverse occurs among the non-negative powers of b.