Unformatted text preview: HA is determined by .h 1 a 1 /.h 2 a 2 / D h 1 ˛ a 1 .h 2 /a 1 a 2 : 5.1.12. Count the number of ways to arrange four red beads, three blue beads, and two yellow beads on a straight wire. 5.1.13. How may elements are there in S 8 of cycle structure 4 2 ? 5.1.14. How may elements are there in S 8 of cycle structure 2 4 ? 5.1.15. How may elements are there in S 12 of cycle structure 3 2 2 3 ? 5.1.16. How may elements are there in S 26 of cycle structure 4 3 3 2 2 4 ? 5.1.17. Let r 1 > r 2 > ::: > r s ³ 1 and let m i 2 N for 1 ´ i ´ s , such that P i m i r i D n . How many elements does S n have with m 1 cycles of length r 1 , m 2 cycles of length r 2 , and so on? 5.1.18. Verify that the formula ± f a 1 ;a 2 ;:::;a k g D f ±.a 1 /;±.a 2 /;:::;±.a k / g does indeed deﬁne an action of S n on the set X of kelement subsets of f 1;2;:::;n g . (See Example 5.1.19 .)...
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 Fall '08
 EVERAGE
 Algebra, Group Theory, Sets, Normal subgroup, Coset, Index of a subgroup, NG .H

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