In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z−1xzz...

the structure of a metric space, given by the so-called word metric. Geometric group theory, as a distinct area, is relatively new, and became a clearly...

word problem for groups; and the classical Burnside problem. See the book by Chandler and Magnus for a detailed history of combinatorial group theory...

Word (computer architecture), a group of bits or digits/characters processed as a unit Word (formal language theory), a finite sequence of letters taken...

In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely...

the Sturm comparison theorem.: 114  Cutting sequence Word (group theory) Morphic word Lyndon word Hordijk, A.; Laan, D. A. (2001). "Bounds for Deterministic...

Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge, in contrast to more common uses of the word "theory" that...

geometry, in the sense of geometric group theory: one has the Cayley graph, which has a metric, called the word metric. These are also two resulting...

of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G {\displaystyle G} is the algorithmic problem...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

In group theory, a word metric on a discrete group G {\displaystyle G} is a way to measure distance between any two elements of G {\displaystyle G} ....

immediate precursor for small cancellation theory: this paper provided a solution of the word problem for a class of groups satisfying a complicated set of combinatorial...

isotopy), and whose group operation is composition of braids (see § Introduction). Example applications of braid groups include knot theory, where any knot...

words (followed by reduction if necessary) as group operation. The identity is the empty word. A reduced word is called cyclically reduced if its first and...

Muted Group Theory (MGT) is a communication theory developed by cultural anthropologist Edwin Ardener and feminist scholar Shirley Ardener in 1975, that...

mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with...

representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which...

mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra:...

In group theory, Matsumoto's theorem, proved by Hideya Matsumoto (1964), gives conditions for two reduced words of a Coxeter group to represent the same...

parts of topology, e.g. knot theory. Algebraic graph theory has close links with group theory and topological graph theory has close links to topology...

Word Processing in Groups is a monograph in mathematics on the theory of automatic groups, a type of abstract algebra whose operations are defined by...

mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains...

A word is a basic element of language that carries meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often...

structure of Galois groups in algebraic number theory to automorphic forms and, more generally, the representation theory of algebraic groups over local fields...

each other. In geometric group theory, a finitely generated group is viewed as a metric space using the word metric. If two groups are (abstractly) commensurable...

The Strauss–Howe generational theory, devised by William Strauss and Neil Howe, is a psychohistorical theory which describes a theorized recurring generation...

linguistics, these are known as phrasemes. In theories of syntax, a phrase is any group of words, or sometimes a single word, which plays a particular role within...

former host of the YouTube series Game Theory, and its spin-off channels Film Theory, Food Theory, and Style Theory, each analyzing various video games,...

word entered the English language in the 16th century from Italian, Spanish, and medieval Latin. Initially, its meaning was restricted to the theory of...

Bass–Serre theory is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms...