MAD 4301 Midterm: MAS4301 C97 Test 2
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Instructions: do not write your answers on this paper, use separate answer sheets. Find an element of order 27, an element of order 6, and and element of order 2. (b) suppose b has order 5 and c has order 8. Find all other idempotents in r. (d) a nilpotent element x of r satis es an equation xn = 0, for some n > 0. Find all other nilpotent elements in r. (4) (20 points) give examples of the following. Then z/m is a eld if and only if m is a prime number. Proof: (6) (15 points) let g be a group and a an element of g. if the order of a is d and af = e, then d|f . Proof: (7) (10 points) let g = {a1, a2, . Proof: (8) (10 points) state and prove the abstract fermat theorem for nite abelian groups.
