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Topic: Quaternion group

	Quaternion - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		The conjugate of a quaternion corresponds to the conjugate transpose of the matrix.
		In this representation, the conjugate of a quaternion corresponds to the transpose of the matrix.
		Quaternions are often used in computer graphics (and associated geometric analysis) to represent rotations (see quaternions and spatial rotation) and orientations of objects in three-dimensional space.
	en.wikipedia.org /wiki/Quaternion (2927 words)

	Quaternion group - Wikipedia, the free encyclopedia
		The quaternion group Q may be regarded as acting on the eight nonzero elements of the 2-dimensional vector space over the finite field GF(3).
		The generalized quaternion groups are members of the still larger family of dicyclic groups.
		The generalized quaternion groups have the property that every abelian subgroup is cyclic.
	en.wikipedia.org /wiki/Quaternion_group (480 words)

	PlanetMath: quaternion group
		The quaternion group, or quaternionic group, is a noncommutative group with eight elements.
		Quaternions were known to Gauss in 1819 or 1820, but he did not publicize this discovery, and quaternions weren't rediscovered until 1843, with Hamilton.
		This is version 8 of quaternion group, born on 2002-04-17, modified 2005-03-18.
	planetmath.org /encyclopedia/QuaternionGroup.html (204 words)

	Quaternion - Open Encyclopedia (Site not responding. Last check: 2007-11-05)
		By linearity, multiplication of quaternions is completely determined by the multiplication table for the basis quaternions; this table is given at the right.
		The conjugate of the quaternion $z = a + bi + cj + dk is defined as$
		Quaternions are often used in computer graphics (and associated geometric analysis) to represent rotations (see quaternions and spatial rotation) and orientations of objects in 3d space.
	open-encyclopedia.com /Quaternion (2712 words)

	Read about Quaternion at WorldVillage Encyclopedia. Research Quaternion and learn about Quaternion here! (Site not responding. Last check: 2007-11-05)
		The algebra of quaternions is ofted denoted by H (for Hamilton), or in
		The conjugate of a quaternion corresponds to the
		In this representation, the conjugate of a quaternion corresponds to the
	encyclopedia.worldvillage.com /s/b/Quaternion (2438 words)

	Quaternion
		A quaternion is a mathematical concept introduced by William Rowan Hamilton of Ireland in 1843.
		By linearity, multiplication of quaternions is completely determined by the multiplication table for the unit quaternions; this table is given at the right.
		Quaternions are sometimes used in computer graphics (and associated geometric analysis) to represent rotations or orientations of objects in 3d space.
	www.brainyencyclopedia.com /encyclopedia/q/qu/quaternion.html (1639 words)

	[No title]
		The quaternion group is isomorphic to the group generated by a, b with presentation a^2 = b^2 = aba^(-1)b^(-1) and a^4 = 1.
		The dihedral group of order 2n is isomorphic to the group generated by a, b with presentation a^2 = b^n = 1 and a b a = b^(-1).
		This is the group with three generators a, b, and c and relations c = a^2 = b^n, ca = ac, bc = cb, ab = ba*c, and c^2 = 1.
	www.win.tue.nl /~amc/oz/om/cds/groupname1.html (236 words)

	Quaternion group -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		In (The branch of mathematics dealing with groups) group theory, the quaternion group is a (Click link for more info and facts about non-abelian) non-abelian ((chemistry) two or more atoms bound together as a single unit and forming part of a molecule) group of order 8 with a number of interesting properties.
		A group is called a generalized quaternion group if it has a (A show or display; the act of presenting something to sight or view) presentation
		The generalized quaternion groups are members of the still larger family of (Click link for more info and facts about dicyclic group) dicyclic groups.
	www.absoluteastronomy.com /encyclopedia/q/qu/quaternion_group.htm (616 words)

	Read about Quaternion group at WorldVillage Encyclopedia. Research Quaternion group and learn about Quaternion group ... (Site not responding. Last check: 2007-11-05)
		In group theory, the quaternion group is a
		Note that this is note quite the group algebra on Q (which would be 8-dimensional).
		The generalized quaternion groups are members of the still larger family of
	encyclopedia.worldvillage.com /s/b/Quaternion_group (377 words)

	Group Library (Site not responding. Last check: 2007-11-05)
		This group is the group of symmetries of a non-square rectangle.
		This group is the group of symmetries of a tetrahedron.
		This group is the group of symmetries of a dodecahedron, and also the group of symmetries of an icosahedron.
	www.platosheaven.com /groupexplorer/groups.html (1656 words)

	Quaternion group (Site not responding. Last check: 2007-11-05)
		In group theory, the quaternion group is a non- abelian group of order 8 with a number of interesting properties.
		Note that the resulting group is non- commutative ; for example ij= -ji.
		Conversely, one can start with the quaternions and define the quaternion group as the multiplicative subgroupconsisting of the eight elements {1, -1, i, -i, j, -j, k,-k}.
	www.therfcc.org /quaternion-group-190436.html (252 words)

	Some group multiplication tables (Site not responding. Last check: 2007-11-05)
		That is, any group of order 2 through 10 is isomorphic to one of the groups given on this page.
		The quaternion group is discussed in Example 3.3.7.
		There are additional group tables at the end of Chapter 7.
	www.math.niu.edu /~beachy/aaol/grouptables1.html (265 words)

	PlanetMath: Hamiltonian quaternions
		The kernel has a geometric interpretation as well: two unit vectors in opposite directions determine the same axis of rotation.
		Cross-references: opposite, unit vectors, cover, subset, kernel, group homomorphism, onto, mapping, composite, angle, line, sphere, permutation, origin, between, group, distributive laws, natural embedding, equality, ring, Euler four-square identity, involution, complex numbers, inverse, conjugate, norm, real numbers, embeddings, obvious, isomorphic, subalgebras, subspaces, order, column, row, basis, dimension, algebra, associative, unital
		This is version 5 of Hamiltonian quaternions, born on 2002-04-17, modified 2004-06-04.
	planetmath.org /encyclopedia/Quaternion.html (236 words)

	normal
		The group of all rotational symmetries of the cube such that the axis of rotation either passes through the center of 2 opposing faces or through 2 opposing vertices.
		For example, the group of 4 rotations of a cube along the x-axis basically "looks the same" as the group of 4 rotations of a cube along the y-axis, or along the z-axis for that matter.
		Groups: 1) group of rotational symmetries of a tetrahedron 2) group of rotational symmetries of a cube (which is effectively the same as that of an octahedron) 3) group of rotational symmetries of an icosahedron (which is effectively the same as that of a dodecahedron)
	math.ucr.edu /home/baez/normal.html (2662 words)

	[No title]
		This symbol represents the quaternion group of order 8.
		This symbol is a function with one argument, which should be a positive integer n.
		This symbol is a function with one argument, which should be a positive integer.
	www.win.tue.nl /~amc/oz/om/cds/groupname1.ocd (200 words)

	Quaternion group normal subgroup distributivity non-abelian subgroup commutative center group inner automorphism group ... (Site not responding. Last check: 2007-11-05)
		Quaternion group normal subgroup distributivity non-abelian subgroup commutative center group inner automorphism group symmetric group dicyclic group
		The quaternion group, often denoted by Q, is usually written in multiplicative form, with the following 8 elements :Q = {1, −1, i, −i, j, −j, k, −k}Here 1 is the identity element, (−1)
		Coxeter, H.S.M. The binary polyhedral groups and other generalizations of the quaternion group.
	en.powerwissen.com /sXjOwar%2BB3Tb0POaIu%2BlHQ%3D%3D_Quarternionic_group.html (480 words)

	Quaternion References
		M.P. Cayley, Arthur: On the quaternion equation qQ — Qq’ = 0.
		Neumann, P.M., Stoy, G.A., and Thompson, E.C. Groups and Geometry.
		Pizer, A. On the arithmetic of quaternion algebras I. Acta Arith.
	home.att.net /~t.a.ell/QuatRef.htm (10852 words)

	Quaternion group - Encyclopedia, History, Geography and Biography
		Quaternion group - Encyclopedia, History, Geography and Biography
		The entire multiplication table for Q is given by:
		Quaternion group, Generalized quaternion group and See also.
	www.arikah.net /encyclopedia/Quaternion_group (475 words)

	The Quaternion Group
		Let a and b be in a group G such that a=b=4, a
		It is well-known that the set W is a group under matrix multiplication, where W consists of 2 by 2 matrices with non-zero determinants.
		Hence this quotient group is abelian and equal to its center.
	www.math.hawaii.edu /~ramsey/Math611/AbstractAlgebra/Q8.htm (1195 words)

	Atlas: On The Minimal Polynomials of the N-Generalized Quaternions by K. Todorov
		Atlas: On The Minimal Polynomials of the N-Generalized Quaternions by K. Todorov
		Multiplication is determined by the rules of the multiplication of the quaternion group \rt
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahn-33.
	atlas-conferences.com /cgi-bin/abstract/cahn-33 (182 words)

	Some non-normal Cayley digraphs of the generalized quaternion group of certain orders (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		Some non-normal Cayley digraphs of the generalized quaternion group of certain orders (ResearchIndex)
		Some non-normal Cayley digraphs of the generalized quaternion group of certain orders (2003)
		9 Permutation groups through invariant relations and invariant..
	citeseer.ist.psu.edu /645537.html (281 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Energy Citations Database (ECD) Document #4098945 - ON ONE REALIZATION OF REPRESENTATIONS OF THE QUATERNION GROUP.
		Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
		GROUP THEORY/representations of quaternion group in, realization of
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=4098945 (95 words)

	IngentaConnect Embedding Obstructions for the Generalized Quaternion Group (Site not responding. Last check: 2007-11-05)
		IngentaConnect Embedding Obstructions for the Generalized Quaternion Group
		In this paper, we examine the obstructions to the solvability of certain embedding problems with the generalized quaternion group over arbitrary fields of characteristic not 2.
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	www.ingentaconnect.com /content/ap/ja/2000/00000226/00000001/art08190 (145 words)

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