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Cyclic Subgroup

  • Definition: An abstract example of a subgroup is the cyclic subgroup generated by an arbitrary element of x of a group G. We use multiplicative notation. The cyclic subgroup H generated by x is the set of all elements that are powers of x: H = {..., x^(-2), x^(-1), 1, x, x^2, ...}.

    Source: Algebra, second edition by Michael Artin

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