(3) Let G be the group Sn. Let S be the 3-fold Cartesian product of {1,...,n}. Describe the orbits of the action of G on S given by g* (81, 82, 83) = (g($1), g($2), g($3)).
(3) Let G be the group Sn. Let S be the 3-fold Cartesian product of {1,...,n}. Describe the orbits of the action of G on S given by g* (81, 82, 83) = (g($1), g($2), g($3)).
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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Abstract Algebra
![(3) Let \( G \) be the group \( S_n \). Let \( S \) be the 3-fold Cartesian product of \(\{1, \ldots, n\}\). Describe the orbits of the action of \( G \) on \( S \) given by
\[
g \star (s_1, s_2, s_3) = (g(s_1), g(s_2), g(s_3)).
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F382d69cf-ffe2-43c0-99c4-21bedf550518%2Fc1c2616f-88d4-47aa-9edb-eb31bfd9a7dc%2Fh4tb7pj_processed.png&w=3840&q=75)
Transcribed Image Text:(3) Let \( G \) be the group \( S_n \). Let \( S \) be the 3-fold Cartesian product of \(\{1, \ldots, n\}\). Describe the orbits of the action of \( G \) on \( S \) given by
\[
g \star (s_1, s_2, s_3) = (g(s_1), g(s_2), g(s_3)).
\]
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