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...

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

the word problem for groups; and the classical Burnside problem. See (Chandler & Magnus 1982) for a detailed history of combinatorial group theory. A proto-form...

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...

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

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...

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

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...

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...

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

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} ....

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

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

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...

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

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...

new word, whose length is the sum of the lengths of the original words. The result of concatenating a word with the empty word is the original word. In...

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called...

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...

of the Keller Fay Group found discussions are often face-to-face and not primarily dominated by social media. Alluding to offline word of mouth (real life...

effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical...

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...

and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood...

information theory. The binary Golay code was developed in 1949. It is an error-correcting code capable of correcting up to three errors in each 24-bit word, and...

geometric group theory, the growth rate of a group with respect to a symmetric generating set describes how fast a group grows. Every element in the group can...

solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof...

prototypical example is the word problem for groups, but there are many other instances as well. A deep result of computational theory is that answering this...

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