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Examples ofabelian group
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For example, every finitely generatedabeliangroupis amenable.
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Since the action is rotation on a compactabeliangroupit has discrete spectrum and entropy zero.
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The final step is to reduce to anabeliangroupextension.
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It is a discreteabeliangroupwith a left -action by multiplication.
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Anabeliangroup(or any commutative monoid) with being the identity morphism.
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A special case is that of anabeliangroupwhere any probability measure is a class function.
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This is anabeliangroupfor all "k".
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This example is from Wikipedia and may be reused under a CC BY-SA license.This is achieved by putting an alternativeabeliangroupstructure on the normal invariants as described here.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Consider theabeliangroup(that is, the set with addition modulo 4), and its subgroup.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Somewhat akin to the dimension of vector spaces, everyabeliangrouphas a "rank".
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This example is from Wikipedia and may be reused under a CC BY-SA license.The number of independent generators is the rank of anabeliangroup.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Briefly, a ring is anabeliangroupwith a second binary operation that is distributive over theabeliangroupoperation and is associative.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Next, one notes that the set of endomorphisms of anabeliangroupis an endomorphism ring.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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