group presentation
31Mobius Artists Group — The Mobius Artists Group is an interdisciplinary group of artists, founded in 1977 by Marilyn Arsem in Boston, Massachusetts as Mobius Theater. It is known for incorporating a wide range of visual, performing and media arts into live performance …
32Modular group — For a group whose lattice of subgroups is modular see Iwasawa group. In mathematics, the modular group Γ is a fundamental object of study in number theory, geometry, algebra, and many other areas of advanced mathematics. The modular group can be… …
33Dicyclic group — In group theory, a dicyclic group (notation Dicn) is a member of a class of non abelian groups of order 4n (n > 1). It is an extension of the cyclic group of order 2 by a cyclic group of order 2n, giving the name di cyclic. In the… …
34Braid group — In mathematics, the braid group on n strands, denoted by B n , is a certain group which has an intuitive geometrical representation, and in a sense generalizes the symmetric group S n . Here, n is a natural number; if n gt; 1, then B n is an… …
35Word (group theory) — 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 1 xzz , and y 1 zxx 1 yz 1 are words in the set { x , y , z }. Words play an important role …
36Coxeter group — In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry …
37Knot group — In mathematics, a knot is an embedding of a circle into 3 dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement of K in R3,:pi 1(mathbb{R}^3 ackslash K).Two equivalent knots have… …
38Dihedral group — This snowflake has the dihedral symmetry of a regular hexagon. In mathematics, a dihedral group is the group of symmetries of a regular polygon, including both rotations and reflections.[1] Dihedr …
39SQ universal group — In mathematics, in the realm of group theory, a countable group is said to be SQ universal if every countable group can be embedded in one of its quotient groups. SQ universality can be thought of as a measure of largeness or complexity of a… …
40Generating set of a group — In abstract algebra, a generating set of a group is a subset that is not contained in any proper subgroup of the group. Equivalently, a generating set of a group is a subset such that every element of the group can be expressed as the combination …
