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A robust fact about 5-cycles
math_explorer 2
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by math_explorer
[quote]Lemma 3. (Barrington, 1986) There are two five-cycles 
and 
in 
whose commutator is a five-cycle. (The commutator of 
and 
is 
.)
Proof.
[/quote]
Someday I want to write a paper and include a lemma with a proof like this.
Uh, is it just me or is this proof actually incorrect...? I keep getting
. I think Mr. Barrington composed his permutations the wrong way. (Fortunately for complexity theory, the lemma is robust to this issue! :P)
and 
in 
whose commutator is a five-cycle. (The commutator of 
and 
is 
.)Proof.
[/quote]Uh, is it just me or is this proof actually incorrect...? I keep getting
. I think Mr. Barrington composed his permutations the wrong way. (Fortunately for complexity theory, the lemma is robust to this issue! :P)
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