The empty semigroup is not monogenic #567
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@wilfwilson this seems to cause some of the GAP tests to fail. Any thoughts? |
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@james-d-mitchell the test failures were unrelated to this PR, and were caused by first this gap-system/gap#3052 and then this gap-system/gap#3053 being merged into GAP master. For the first, this caused our So (having changed nothing about this PR), the tests on this should pass now. |
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Thanks @wilfwilson ! |
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Currently, an empty semigroup is set to be monogenic by an immediate method. But I don't think that it should count as monogenic: its rank isn't 1, and there exists no element inside the empty semigroup that generates the empty semigroup.
I know that we normally avoid empty semigroups, and for certain properties it's probably not very clear whether the empty semigroup has that property. But here I think it's clear so we may as well fix it.