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True/False, explain: 1. If G is a finite group and G28, then there is a subgroup...

True/False, explain:
1. If G is a finite group and G28, then there is a subgroup of G of order 2401=74

2. If |G|=19, then G is isomorphic to Z19.

3. If F subset of K is a degree 5 field extension, any element b in K is the root of some polynomial p(x) in F[x]

4. If F subset of K is a degree 5 field extension, viewing K as a vector space over F, Aut(K, F) consists of all F-linear transformations of K.

5. Suppose f in F[x] and F in K is a degree 5 field extension. Then Aut(K, F) permutes the roots of f in K.

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