need help with 7c and 7d please (b) a4 (c) as (d) 011 6. In 44 what are (os)80 a

Question

need help with 7c and 7d please

(b) a4 (c) as (d) 011 6. In 44 what are (os)80 and (as)80? 7. Let G be a group of permutations on a set X and let a E X. Define stab(a) many elements are in stab(a) in the following situations? (a) X = { 1, 2, 3), a-2. (b) X= {1,2,3}, a= 3. (c) X= {1, 2, 3, 4), a -2. (d) X = {1, 2.3.4.5), a 2. (e) X-{ 1, 2, 3, 4, 5, 6, 7, 8,9), a=2. [Hint: Use factorials and generali 8. Let -(135792468) E Sg. (a) What is the smallest positive i so that o (b) What is the smallest positive i so that aa?

Explanation / Answer

7(c) 4P2 = 4!/2! = 4*3*2*1/2*1 = 12

7(d) 5P2 = 5!/2! = 5*4*3*2*1/2*1 = 60

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