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...

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...

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...

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

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

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...

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...

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...