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MAT 312/AMS 351 – Fall 2010
Homework 9
1. Calculate the order of the permutation
π
=
p
1 2 3 4 5 6 7 8
4 6 1 8 2 5 7 3
P
.
Hint: write it Frst in cycle notation.
2. Same question for
π
=
p
1 2 3 4 5 6 7 8
4 1 5 7 6 3 8 2
P
.
3. Give a conjugacy
σ
relating
π
1
= (1547)(263) to
π
2
= (123)(4567), so
that
π
2
=
σπ
1
σ

1
. Check that it works.
4. Prove that two conjugate permutations have the same order.
5. Break up S(5) into conjugacy classes (following our work in class with
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This note was uploaded on 12/19/2010 for the course AMS 351 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Staff

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