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symmetric and alternating groups

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The conjugacy classes in Sn correspond to partitions of n, and are determined by cycle structure.

Which conjugacy classes of Sn that are in An split into two conjugacy classes in An? Please give a necessary and sufficient condition.

Sn is the symmetric group of degree n, and An is the alternating group of degree n.

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Solution Summary

This solution explains how to solve the given problem involving conjugacy classes.