In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset {...

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...

In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of odd...

MR 1878556 "Galois group", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Galois group and the Quaternion group "Galois Groups". MathPages.com. Comparing...

used to represent rotation, unit quaternions are also called rotation quaternions as they represent the 3D rotation group. When used to represent an orientation...

In mathematics, a versor is a quaternion of norm one (a unit quaternion). Each versor has the form q = exp ⁡ ( a r ) = cos ⁡ a + r sin ⁡ a , r 2 = − 1...

The Quaternion Eagle (German: Quaternionenadler; Italian: aquila quaternione), also known as the Imperial Quaternion Eagle (German: Quaternionen-Reichsadler)...

the four-group is the basic group of permutations in the twelve-tone technique. In that instance, the Cayley table is written Quaternion group List of...

2-group. However, every group of order p2 is abelian. The dihedral groups are both very similar to and very dissimilar from the quaternion groups and...

non-abelian groups of order 2n which have a cyclic subgroup of index 2. Two are well known, the generalized quaternion group and the dihedral group. One of...

finite p-groups are solvable, as all finite p-groups are nilpotent. In particular, the quaternion group is a solvable group given by the group extension...

quaternion in Wiktionary, the free dictionary. The quaternions form a number system that extends the complex numbers. Quaternion rotation Quaternion group...

quaternions with norm 1 (the versors), as a multiplicative group, act on R3: for any such quaternion z = cos α/2 + v sin α/2, the mapping f(x) = zxz* is a...

In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a...

In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus...

In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were...

The Poincaré group, named after Henri Poincaré (1906), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It...

of class 1). The 2-groups of maximal class are the generalised quaternion groups, the dihedral groups, and the semidihedral groups. Furthermore, every...

variants thereof, and the elements of {1, i, j, k} multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions...

non-abelian Dedekind group is called a Hamiltonian group. The most familiar (and smallest) example of a Hamiltonian group is the quaternion group of order 8, denoted...

A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that...

mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists at...

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...

S^{3}} ; as a group, it may be identified with the group of unit quaternions. The Heisenberg group is a connected nilpotent Lie group of dimension 3...

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...

group is isomorphic to the quaternion group Q. More generally, when n is a power of 2, the dicyclic group is isomorphic to the generalized quaternion...

Galois group Gell-Mann matrices Group object Hilbert space Integer Lie group Matrix Modular arithmetic Number Pauli matrices Real number Quaternion Quaternion...

In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations...

In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it...

In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of...