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....
2 KB (237 words) - 08:00, 17 August 2024
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...
36 KB (4,113 words) - 03:36, 18 July 2024
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...
11 KB (1,599 words) - 00:07, 8 July 2024
just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study...
15 KB (1,831 words) - 21:48, 27 January 2024
to n. This group, usually denoted ( Z / n Z ) × {\displaystyle (\mathbb {Z} /n\mathbb {Z} )^{\times }} , is fundamental in number theory. It is used...
26 KB (3,162 words) - 11:41, 6 July 2024
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...
10 KB (1,284 words) - 02:41, 16 July 2024
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...
36 KB (5,284 words) - 20:43, 1 August 2024
automorphism group Quotient group Examples of groups Abelian group Cyclic group Rank of an abelian group Dicyclic group Dihedral group Divisible group Finitely...
10 KB (800 words) - 20:17, 10 January 2024
such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G {\displaystyle...
46 KB (6,130 words) - 06:34, 24 May 2024
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...
1 KB (194 words) - 23:34, 12 August 2023