a cyclically ordered group is a set with both a group structure and a cyclic order, such that left and right multiplication both preserve the cyclic order...

a cyclically ordered group is cyclic. A metacyclic group is a group containing a cyclic normal subgroup whose quotient is also cyclic. These groups include...

integrally closed. Cyclically ordered group – Group with a cyclic order respected by the group operation Linearly ordered group – Group with translationally...

requirement results in a partial cyclic order. A set with a cyclic order is called a cyclically ordered set or simply a cycle.[nb] Some familiar cycles are discrete...

generalisation of this has been recently announced. Cyclically ordered group Hahn embedding theorem Partially ordered group Deroin, Navas & Rivas 2014, 1.1.1. Levi...

orderings. Every subfield of an ordered field is also an ordered field in the inherited order. Every ordered field contains an ordered subfield that is isomorphic...

finitely generated abelian groups. The subgroups of a primary cyclic group are linearly ordered by inclusion. The only other groups that have this property...

In group theory, especially, in geometric group theory, the class of free-by-cyclic groups have been deeply studied as important examples. A group G {\displaystyle...

cyclic. in the study of infinite groups, a Z-group is a group which possesses a very general form of central series. in the study of ordered groups,...

with a cyclic order Necklace (combinatorics), an equivalence classes of cyclically ordered sequences of symbols modulo certain symmetries Cyclic (mathematics)...

set equipped with a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, toset and loset are also used. The term...

mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer...

mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvability...

well order, well ordered, and well ordering. Every non-empty well-ordered set has a least element. Every element s of a well-ordered set, except a possible...

In mathematics, an ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the...

generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders. There are...

particular group is abelian, whenever both abelian and non-abelian groups are considered, with some notable exceptions being near-rings and partially ordered groups...

wikidata descriptions as a fallback Ordered field – Algebraic object with an ordered structure Ordered group – Group with a compatible partial orderPages...

In mathematics, the cyclic category or cycle category or category of cycles is a category of finite cyclically ordered sets and degree-1 maps between them...

In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice...

specifically in order theory, several different types of ordered set have been studied. They include: Cyclic orders, orderings in which triples of elements are...

free group with ordered basis [ x1, …, xn ] is generated by the following 4 elementary Nielsen transformations: Switch x1 and x2 Cyclically permute x1, x2...

or shift cyclically when they are multiplied by another integer n {\displaystyle n} . Examples are: 142857 × 3 = 428571 (shifts cyclically one place...

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...

totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set,...

largest ordered set that is complete and locally Archimedean. As with the previous two examples, this set is no longer a field or additive group. Ordered fields...

{\displaystyle a^{-1}} ⁠. Formally, a group is an ordered pair of a set and a binary operation on this set that satisfies the group axioms. The set is called the...

Prüfer group. The Prüfer p-group is the unique infinite p-group that is locally cyclic (every finite set of elements generates a cyclic group). As seen...

permutation action of the symmetric group on n {\displaystyle n} strands operating on the indices of coordinates. That is, an ordered n {\displaystyle n} -tuple...

subgroups of a group is the lattice defined by its subgroups, partially ordered by set inclusion. locally cyclic group A group is locally cyclic if every finitely...