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Added in “finite” unions since ideals do not have to be complete to generate a dual filter. Tags: Mobile edit Mobile app edit iOS app edit |
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==Construction of filters on a group==
A filter on a group can be constructed from an invariant ideal on of the [[Boolean algebra]] of subsets of ''A'' containing all elements of ''A''. Here an ideal is a collection ''I'' of subsets of ''A'' closed under taking finite unions and subsets, and is called invariant if it is invariant under the action of the group ''G''. For each element ''S'' of the ideal one can take the subgroup of ''G'' consisting of all elements fixing every element ''S''. These subgroups generate a normal filter of ''G''.
==References==
*{{citation|last=Fraenkel|first= A.
|title=Der Begriff "definit" und die Unabhängigkeit des Auswahlaxioms|
|journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften|year= 1922|pages= 253–257 }}
*{{citation|first= Andrzej |last=Mostowski|title= Über den Begriff einer Endlichen Menge|year=1938|journal= Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III|volume=31|issue=8|pages=13–20}}
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