Exercise 3.1.19 Show that, for n>3, the group A, is generated by 3-cycles (abc).
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Chapter2: Second-order Linear Odes
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3.1.19
Transcribed Image Text:Exercise 3.1.19 Show that, for n>3, the group A, is generated by 3-cycles (abc).
Hint. We know that Sn is generated by 2-cycles. So we just need to think about prod-
ucts of two 2-cycles. There are three cases to consider. (ab)(ab), (ab)(ac), (ab)(cd), where
a, b, c, d are pairwise distinct integers from {1, ..., n}. For the last case, look at: (ab)(bc)
(bc)(cd).
Expert Solution
Step 1
claim- show that for the group is generated by
to prove that is generated by , we only need to prove that
that is,
can be written as compositions of three cycle.
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