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Every word is conjugate to a cyclically reduced word. The cyclically reduced words are minimal-length representatives of the conjugacy classes in the free group. This representative is not uniquely determined, but it is unique up to cyclic shifts (since every cyclic shift is a conjugate element).
Printable version; In other projects ... This is a list of recurring ... Cyclic process – Carnot cycle – Double-slit experiment – Dynamic theory of gravity ...
Cyclic group, a group generated by a single element; Cyclic homology, an approximation of K-theory used in non-commutative differential geometry; Cyclic module, a module generated by a single element; Cyclic notation, a way of writing permutations; Cyclic number, a number such that cyclic permutations of the digits are successive multiples of ...
A thesaurus (pl.: thesauri or thesauruses), sometimes called a synonym dictionary or dictionary of synonyms, is a reference work which arranges words by their meanings (or in simpler terms, a book where one can find different words with similar meanings to other words), [1] [2] sometimes as a hierarchy of broader and narrower terms, sometimes simply as lists of synonyms and antonyms.
A cyclic permutation consisting of a single 8-cycle. There is not widespread consensus about the precise definition of a cyclic permutation. Some authors define a permutation σ of a set X to be cyclic if "successive application would take each object of the permuted set successively through the positions of all the other objects", [1] or, equivalently, if its representation in cycle notation ...
Cycle, a set equipped with a cyclic order. Necklace (combinatorics), an equivalence classes of cyclically ordered sequences of symbols modulo certain symmetries; Cyclic (mathematics), a list of mathematics articles with "cyclic" in the title; Cyclic group, a group generated by a single element
The additive group of rational numbers (Q, +) is locally cyclic – any pair of rational numbers a/b and c/d is contained in the cyclic subgroup generated by 1/(bd). [2]The additive group of the dyadic rational numbers, the rational numbers of the form a/2 b, is also locally cyclic – any pair of dyadic rational numbers a/2 b and c/2 d is contained in the cyclic subgroup generated by 1/2 max ...
In contrast, (Z/8Z) × = {1, 3, 5, 7} is a Klein 4-group and is not cyclic. When (Z/nZ) × is cyclic, its generators are called primitive roots modulo n. For a prime number p, the group (Z/pZ) × is always cyclic, consisting of the non-zero elements of the finite field of order p. More generally, every finite subgroup of the multiplicative ...
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