Let S, denote the symmetric group on n letters and let p and q be prime...
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Let S, denote the symmetric group on n letters and let p and q be prime numbers. (a) What is the smallest n such that S₁, has an element of order p? (b) What is the smallest n such that S₁, has an element of order p²? (c) What is the smallest n such that S₁, has an element of order pq? 112 (d) EXTRA CREDIT: Suppose m is a composite number and let m = pp²p be its prime decomposition. Find the smallest n such that S, has an element of order m. Let S, denote the symmetric group on n letters and let p and q be prime numbers. (a) What is the smallest n such that S₁, has an element of order p? (b) What is the smallest n such that S₁, has an element of order p²? (c) What is the smallest n such that S₁, has an element of order pq? 112 (d) EXTRA CREDIT: Suppose m is a composite number and let m = pp²p be its prime decomposition. Find the smallest n such that S, has an element of order m.
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a The smallest n such that Sn has an element of order p is np From the definition of the symmetric g... View the full answer
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
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