8) Let A be a nonempty set and k be a positive integer with k < |A|. The symmetric group SĄ acts on the set B consisting of all subsets of A of cardinality k by o · {a, ..., ak} = {o(a,), ...,o(ar)}. %3D a) Prove that this is a group action. b) Describe explicitly how the elements (1 2) and (1 2 3 ) act on the six 2-element subsets of {1,2,3,4}.
8) Let A be a nonempty set and k be a positive integer with k < |A|. The symmetric group SĄ acts on the set B consisting of all subsets of A of cardinality k by o · {a, ..., ak} = {o(a,), ...,o(ar)}. %3D a) Prove that this is a group action. b) Describe explicitly how the elements (1 2) and (1 2 3 ) act on the six 2-element subsets of {1,2,3,4}.
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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Transcribed Image Text:8) Let A be a nonempty set and k be a positive integer with k < |A|. The symmetric group Sa acts on
the set B consisting of all subsets of A of cardinality k by o · {a,, ...,ar} = {o(a,), ...,o (ar)}.
a) Prove that this is a group action.
b) Describe explicitly how the elements (1 2) and (1 2 3) act on the six 2-element subsets of
{1,2,3,4}.
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