definition is that a number n is cyclic if and only if any group of order n is cyclic. Any prime number is clearly cyclic. All cyclic numbers are square-free....

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...

A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the...

just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study...

to n. This group, usually denoted ( Z / n Z ) × {\displaystyle (\mathbb {Z} /n\mathbb {Z} )^{\times }} , is fundamental in number theory. It is used...

specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number of elements...

algebra. Any group of prime order is isomorphic to a cyclic group and therefore abelian. Any group whose order is a square of a prime number is also abelian...

automorphism group Quotient group Examples of groups Abelian group Cyclic group Rank of an abelian group Dicyclic group Dihedral group Divisible group Finitely...

such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G {\displaystyle...

a primary cyclic group is a group that is both a cyclic group and a p-primary group for some prime number p. That is, it is a cyclic group of order pm...