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It's true that S3 can be generated by A = {a₁ = (12), a2 = (23)}. Show that S3 has an element that cannot be written as aan or anar for n, m € Z. Thus conclude description of (A) for abelian groups on page 63 cannot be used for that the more-compact non-abelian groups.

It's true that S3 can be generated by A = {a₁ = (12), a2 = (23)}. Show that S3 has an element that cannot be written as aan or anar for n, m € Z. Thus conclude description of (A) for abelian groups on page 63 cannot be used for that the more-compact non-abelian groups.

Advanced Engineering Mathematics
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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It's true that S3 can be generated by A = {a₁ = (12), a2 = (23)}. Show that S3 has an element that cannot be written as a am or anam for n, m € Z. Thus conclude description of (A) for abelian groups on page 63 cannot be used for that the more-compact non-abelian groups.
Transcribed Image Text:It's true that S3 can be generated by A = {a₁ = (12), a2 = (23)}. Show that S3 has an element that cannot be written as a am or anam for n, m € Z. Thus conclude description of (A) for abelian groups on page 63 cannot be used for that the more-compact non-abelian groups.
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