please do 7 and 24
7. 8. Write the class equation for S5 and for A5. If a square remains fixed in the plane, how many square be colored if three colors are used?
24. Let G be a group with order p” where p is prime and X a finite G-set. If XG = {re X: gr = r for all ge G} is the set of elements in X fixed by the group action, then prove that X\ = |XG| (mod p). 25. If G is a group of order p”, where p is prime and n > ? show that munt h
7. 8. Write the class equation for S5 and for A5. If a square remains fixed in the plane, how many square be colored if
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7. 8. Write the class equation for S5 and for A5. If a square remains fixed in the plane, how many square be colored if
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