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(a) Let a and b be two elements of Sn with the same cycle structure. Explain how to produce an element g of Sn which conjugates a to b. (b) Show that even if a and b belong to An, we cannot always take g € An.

(a) Let a and b be two elements of Sn with the same cycle structure. Explain how to produce an element g of Sn which conjugates a to b. (b) Show that even if a and b belong to An, we cannot always take g € An.

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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(5) (a) Let \( a \) and \( b \) be two elements of \( S_n \) with the same cycle structure. Explain how to produce an element \( g \) of \( S_n \) which conjugates \( a \) to \( b \). (b) Show that even if \( a \) and \( b \) belong to \( A_n \), we cannot always take \( g \in A_n \).
Transcribed Image Text:(5) (a) Let \( a \) and \( b \) be two elements of \( S_n \) with the same cycle structure. Explain how to produce an element \( g \) of \( S_n \) which conjugates \( a \) to \( b \). (b) Show that even if \( a \) and \( b \) belong to \( A_n \), we cannot always take \( g \in A_n \).
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