Problem 4 Let o = (4573) and T = (46823) denote permutations in Sg (a.) Calculate the disjoint cycle decomposition for OT (b.) Find the order for OT (c.) Find all generators for (or) ≤ Sg. Express your answers in terms of (7)k for approrpriate k, no need to calculate the disjoint cycle decomposition for these generators.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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Problem 4
Let o = (4573) and 7 = (46823) denote permutations in Sg
(a.) Calculate the disjoint cycle decomposition for σT
(b.) Find the order for OT
(c.) Find all generators for (or) ≤ Sg. Express your answers in terms of (o)k for approrpriate k, no need
to calculate the disjoint cycle decomposition for these generators.
Transcribed Image Text:Problem 4 Let o = (4573) and 7 = (46823) denote permutations in Sg (a.) Calculate the disjoint cycle decomposition for σT (b.) Find the order for OT (c.) Find all generators for (or) ≤ Sg. Express your answers in terms of (o)k for approrpriate k, no need to calculate the disjoint cycle decomposition for these generators.
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