Let S be a Fermat surface of degree 5 and let k be an algebraically closed field of characteristic p = 2. We give a fibration ƒ: S → P with upper limit 1 and lower limit k, and investigate the geometric properties of fiber of ƒ. Furthermore, we investigate the fibration-preserving automorphisms group AutPwith upper limit 1 and lower limit k(S) of ƒ. We obtain that AutPwith upper limit 1 and lower limit k(S) is a p-group of order 256.
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