Hello!

Could anyone help me with the following problem?

Assume that L/K is a finite field extension with degree d and that there are automorphism b_1,…,b_d on L whose restriction to K is equal to id_K and which satisfy the following property: b_i(k) is not equal to b_j(k) if i is not equal to j. Then one has L=K(k).

Does anybody have an idea??