enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Cyclic number - Wikipedia

    en.wikipedia.org/wiki/Cyclic_number

    Cyclic numbers are related to the recurring digital representations of unit fractions. A cyclic number of length L is the digital representation of 1/(L + 1). Conversely, if the digital period of 1/p (where p is prime) is p − 1, then the digits represent a cyclic number. For example: 1/7 = 0.142857 142857...

  3. Cyclic number (group theory) - Wikipedia

    en.wikipedia.org/wiki/Cyclic_number_(group_theory)

    A cyclic number [1] [2] is a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic if and only if any group of order n is cyclic. [3] Any prime number is clearly cyclic. All cyclic numbers are square-free. [4] Let n = p 1 p 2 …

  4. Multiplicative group of integers modulo n - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_group_of...

    For powers of 2 the factor (/) is not cyclic unless k = 0, 1, 2, but factors into cyclic groups as described above. The order of the group φ ( n ) {\displaystyle \varphi (n)} is the product of the orders of the cyclic groups in the direct product.

  5. Cyclic (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Cyclic_(mathematics)

    Cyclic number, a number such that cyclic permutations of the digits are successive multiples of the number; Cyclic order, a ternary relation defining a way to arrange a set of objects in a circle; Cyclic permutation, a permutation with one nontrivial orbit; Cyclic polygon, a polygon which can be given a circumscribed circle; Cyclic shift, also ...

  6. Subgroups of cyclic groups - Wikipedia

    en.wikipedia.org/wiki/Subgroups_of_cyclic_groups

    In abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order n, every subgroup's order is a divisor of n, and there is exactly one subgroup for each divisor. [1] [2] This result has been called the fundamental theorem of cyclic groups. [3] [4]

  7. Cycle index - Wikipedia

    en.wikipedia.org/wiki/Cycle_index

    A cyclic group, C n is the group of rotations of a regular n-gon, that is, n elements equally spaced around a circle. This group has φ(d ) elements of order d for each divisor d of n, where φ(d ) is the Euler φ-function, giving the number of natural numbers less than d which are relatively prime to d.

  8. Ideal class group - Wikipedia

    en.wikipedia.org/wiki/Ideal_class_group

    The number of ideal classes (the class number of R) may be infinite in general. In fact, every abelian group is isomorphic to the ideal class group of some Dedekind domain. [1] But if R is a ring of algebraic integers, then the class number is always finite. This is one of the main results of classical algebraic number theory.

  9. Cyclically ordered group - Wikipedia

    en.wikipedia.org/wiki/Cyclically_ordered_group

    Since a linear order induces a cyclic order, cyclically ordered groups are also a generalization of linearly ordered groups: the rational numbers Q, the real numbers R, and so on. Some of the most important cyclically ordered groups fall into neither previous category: the circle group T and its subgroups , such as the subgroup of rational points .