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The cyclic group of order 12 acts on {1,2,..., 12} with the following cycle structure. (1) (**)(**)(**)(**)(**)(**) 1× ***)(* **)(***)(***) 2 × (****)(****)(****) (******)(******) (************) 1 x 2 x 2 x 4 x Determine the number of different colored necklaces with 12 beads when each bead is colored with one of 3 colors.

The cyclic group of order 12 acts on {1,2,..., 12} with the following cycle structure. (1) (**)(**)(**)(**)(**)(**) 1× ***)(* **)(***)(***) 2 × (****)(****)(****) (******)(******) (************) 1 x 2 x 2 x 4 x Determine the number of different colored necklaces with 12 beads when each bead is colored with one of 3 colors.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The cyclic group of order 12 acts on {1,2, ... , 12} with the following cycle structure. (1) (**)(**)(**)(**)(**)(**) 1x (***)(* **)(***)(***) (****)(****)(****) (******)(******) 1 x 2 x 2 x 2 x (************) 4 x Determine the number of different colored necklaces with 12 beads when each bead is colored with one of 3 colors.
Transcribed Image Text:The cyclic group of order 12 acts on {1,2, ... , 12} with the following cycle structure. (1) (**)(**)(**)(**)(**)(**) 1x (***)(* **)(***)(***) (****)(****)(****) (******)(******) 1 x 2 x 2 x 2 x (************) 4 x Determine the number of different colored necklaces with 12 beads when each bead is colored with one of 3 colors.
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