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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 11E: 11. Assume that are subgroups of the abelian group such that the sum is direct. If is a subgroup...

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Question

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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