Generator-offset property: Difference between revisions
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# ''S'' is of the form ''ax by bz'' for some permutation (''x'', ''y'', ''z'') of (L, M, s). | # ''S'' is of the form ''ax by bz'' for some permutation (''x'', ''y'', ''z'') of (L, M, s). | ||
# The cardinality (size) of ''S'' is either odd, or 4 (and ''S'' is of the form ''xyxz''). | # The cardinality (size) of ''S'' is either odd, or 4 (and ''S'' is of the form ''xyxz''). | ||
[Note: This is not true with ASGC replaced with AG; [[blackdye]] is a counterexample that is MV4.] | |||
==== Proof ==== | ==== Proof ==== | ||
Assuming ASGC, we have two chains of generator ''g''<sub>0</sub> (going right). The two cases are: | Assuming ASGC, we have two chains of generator ''g''<sub>0</sub> (going right). The two cases are: | ||