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The quaternion group is one of the two non-Abelian groups of the five total finite groups of order 8. It is formed by the quaternions +/-1, +/-i, +/-j, and +/-k , denoted Q_8 ...
The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along ...
A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...
The conjugate of a quaternion a=a_1+a_2i+a_3j+a_4k is defined by a^_=a_1-a_2i-a_3j-a_4k.
The norm n(a) of a quaternion a=a_1+a_2i+a_3j+a_4k is defined by n(a)=sqrt(aa^_)=sqrt(a^_a)=sqrt(a_1^2+a_2^2+a_3^2+a_4^2), where a^_=a_1-a_2i-a_3j-a_4k is the quaternion ...
A quaternion Kähler manifold is a Riemannian manifold of dimension 4n, n>=2, whose holonomy is, up to conjugacy, a subgroup of Sp(n)Sp(1)=Sp(n)×Sp(1)/Z_2, but is not a ...
There are two definitions of a metacyclic group. 1. A metacyclic group is a group G such that both its commutator subgroup G^' and the quotient group G/G^' are cyclic (Rose ...
A group that has a primitive group action.
The group theoretical term for what is known to physicists, by way of its connection with matrix traces, as the trace. The powerful group orthogonality theorem gives a number ...
The commutator subgroup (also called a derived group) of a group G is the subgroup generated by the commutators of its elements, and is commonly denoted G^' or [G,G]. It is ...
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