Solution
= Solution
Over $\mathbb F_7$, the <polynomial> $t^4-1$ factors as $(t-1)(t+1)(t^2+1)$. Since $-1$ is not a square modulo $7$, the last factor is an <irreducible polynomial>. The <splitting field> is $\mathbb F_{49}$, so $\boxed{\operatorname{Gal}(t^4-1/\mathbb F_7)\cong C_2}$. The <finite-field Frobenius automorphism> fixes $1,-1$ and swaps the other two roots.