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Cyclic Group

  • Definition: Let G be a group; let x be an element of G. We denote the inverse of x by x^(-1). The symbol x^n denotes the n-fold product of x with itself, x^(-n) the n-fold product of x^(-1) with itself, and x^0 denotes the identity element of G If the set of all elements of the form x^m, for m an integer, equals G, then G is said to be a cyclic group, and x is said to be a generator of G.

    Source: Topology (second edition) by James R. Munkres

  • Listed under: Algebraic Topology, Abstract Algebra

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