Axioms for function semigroups with agreement quasi-order

Stokes, Tim

doi:10.1007/s00012-011-0152-1

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Definitions and Basic Properties1

∀X ∈ X : F (X) = G(x) → H(x) = K(x)1

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2013

2015

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Cited by 2 publications

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“…Next we prove the converse, namely that every (faithful) group with fix-order arises in this way. This was proved in a far more general setting in [3], but only in the faithful case, and in any case, the group proof is rather simpler and we give it here for completeness.…”

Section: Definitions and Basic Propertiesmentioning

confidence: 90%

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Groups with fix-set quasi-order

2015

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Abstract. If X is a set, the fix-set quasiorder on a group of permutations of X is the quasiorder induced by containment of the fix-sets of elements of S X . Axioms for such quasiorders on groups have previously been given. We generalise these to allow non-faithful group actions, the resulting abstract quasiorders being called fix-orders. We characterise the possible fix-orders on a given group G in terms of certain families of subgroups of G. The special case in which the members of the defining family of subgroups are all normal is considered. Software is used to construct and analyse the lattices of fix-orders of many small finite groups.

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Section: Definitions and Basic Propertiesmentioning

confidence: 90%

“…In [3], it was claimed that by dropping Law (1.1) above, the resulting axioms capture the fix-set quasi-order on groups acting (perhaps non-faithfully) on the right of a set X, defined as above but with Fix(g) = {x ∈ X | x · g = x}.…”

Section: ∀X ∈ X : F (X) = G(x) → H(x) = K(x)mentioning

confidence: 99%