Generator-offset property: Difference between revisions
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# It is ''not'' SV3 | # It is ''not'' SV3 | ||
# It is ''not'' chiral | # It is ''not'' chiral | ||
Note that x<sup>''r''</sup>yx<sup>''r''</sup>z (generator x, offset x<sup>''r''</sup>y) is a counterexample to the claim that the offset must be an odd number of steps. | Note that x<sup>''r''</sup>yx<sup>''r''</sup>z (generator x, offset x<sup>''r''</sup>y) is a counterexample to the claim that the offset must be an odd number of steps. | ||
==== Proof ==== | |||
(1) and (2) were proved in the proof of Proposition 1 (the part that we appeal to, from "all multiples of the generator g must be an even number of steps ..." to "These are all distinct by Z-linear independence", does not rely on SGA property). (3) is easy to check using (1). | |||
=== Theorem 4 (Classification of PWF scales) === | === Theorem 4 (Classification of PWF scales) === | ||