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...

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 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...

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...

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

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...