34. Consider the action of S, the symmetric group of order 4, on Z[x1, X2, X3, X4] given by Let Hc S, denote the cyclic subgroup generated by (1423). Then, the cardinality of the orbit O,(x,x, +x,) of H on the polynomial x,x, + xx, is (a) 1 (c) 3 (b) 2 (d) 4
34. Consider the action of S, the symmetric group of order 4, on Z[x1, X2, X3, X4] given by Let Hc S, denote the cyclic subgroup generated by (1423). Then, the cardinality of the orbit O,(x,x, +x,) of H on the polynomial x,x, + xx, is (a) 1 (c) 3 (b) 2 (d) 4
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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![34. Consider the action of S, the symmetric group of order
4, on Z[x,, x2, X3, X4] given by
Oe S,.
Let Hc S, denote the cyclic subgroup generated by
(1423). Then, the cardinality of the orbit O,(x,x3+xx)
of H on the polynomial x,x, + x,X4 is
(a) 1
(c) 3
(b) 2
(d) 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc616de1-d4d7-4e33-8032-527a9d393ee4%2Fdce65bf5-21f6-4587-9210-55cff5f3ca65%2F0ixgfhp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:34. Consider the action of S, the symmetric group of order
4, on Z[x,, x2, X3, X4] given by
Oe S,.
Let Hc S, denote the cyclic subgroup generated by
(1423). Then, the cardinality of the orbit O,(x,x3+xx)
of H on the polynomial x,x, + x,X4 is
(a) 1
(c) 3
(b) 2
(d) 4
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