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Topic: Glossary of group theory

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List of group theory topics

Group (mathematics)

Abelian group

Subgroup

Group isomorphism

Group theory

List of small groups

Glossary of field theory

Direct product

Glossary of ring theory

List of lists of mathematical topics

Glossary of tensor theory

Binary operation

Abstract algebra

Glossary

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	Group theory
		Group theory is that branch of mathematics concerned with the study of groups.
		Groups are used throughout mathematics and the sciences, often to capture the internal symmetry of other structures, in the form of automorphism groups.
		In algebraic topology, groups are used to describe invariants of topological spaces (the name of the torsion subgroup of an infinite group shows the legacy of this field of endeavor).
	www.fact-index.com /g/gr/group_theory_1.html (674 words)

	Glossary of group theory - Wikipedia, the free encyclopedia
		It is the preimage of the identity in the codomain of a group homomorphism.
		Every finite group is built up from simple groups through the use of group extensions, so the study and classification of finite simple groups is central to the study of finite groups in general.
		A group representation is a homomorphism from a group to a general linear group.
	en.wikipedia.org /wiki/Glossary_of_group_theory (845 words)

	Group theory - Wikipedia, the free encyclopedia
		Groups are used throughout mathematics, often to capture the internal symmetry of other structures, in the form of automorphism groups.
		A common foundation for the theory of equations on the basis of the group of permutations was found by mathematician Lagrange (1770, 1771), and on this was built the theory of substitutions.
		Group theory is also very important to the field of chemistry, where it is used to assign symmetries to molecules.
	en.wikipedia.org /wiki/Group_theory (1362 words)

	Glossary of learning theory
		Behaviourism is a psycological theory and practice which is focused on observable behaviour and the influence of conditioning such as operant conditioning and reinforcement of that behaviour (Van Aardweg 1993: 30-31).
		It is intended as a general theory of learning which states that a particular combination of stimuli associated with a movement will on its recurrence cause that movement to follow as an active response, and will therefore lead to a change in behaviour (Open Learning Technology Corporation 1996).
		In most theories of learning, motivation is regarded as a crucial concept which is related to (affective) aspects of learning such as anxiety, and cognitive aspects such as the achievement of goals (Open Learning Technology Corporation 1996).
	hagar.up.ac.za /catts/learner/ameyer/glossaryoflearningtheory.htm (1239 words)

	Glossary of Terms: Th
		The separation of theory and practice, which has its origins in the rupture of society into classes, means speculation in theory and unconscious activity in practice.
		Marxism understands theory uniquely because while materialism supports the existence of a material world outside consciousness, it neglects the active role of the subject in forming the world into objects.
		The theory of marginal utility was developed independently William Stanley Jevons (England 1871), Karl Menger (Austria 1871) and Leon Walras (Switzerland, 1874) and formed the foundation for all subsequent bourgeois economic science.
	www.marxists.org /glossary/terms/t/h.htm (3642 words)

	glossary
		A theory used to justify the termination of a foetus if the intention is to save the life of the mother and the action has the a secondary effect of killing the foetus.
		Theories which centre on the importance, rights or centrality of the individual as opposed to communitarianism which focuses on those of the group.
		A theory popular in the 17th and 18th which holds that it is possible to determine what truly exists by reason alone, and that all things are explicable using reason.
	www.rsweb.org.uk /ethics/glossary.html (5164 words)

	Evolution: Glossary
		Mendelian inheritance is an atomistic theory because in it, inheritance is controlled by distinct genes.
		A group at any level in the classificatory hierarchy, such as a family, is formed by combining a subgroup at the next lowest level (the genus, in this case) with the subgroup or subgroups with which it shares its most recent common ancestor.
		To be exact, it permits paraphyletic groups (which are allowed in phenetic but not in cladistic classification) and monophyletic groups (which are allowed in both cladistic and phenetic classification) but excludes polyphyletic groups (which are banned from cladistic classification but permitted in phenetic classification).
	www.pbs.org /wgbh/evolution/library/glossary/index.html (13331 words)

	Wikinfo \| Group theory
		There are three historical roots of group theory: theory of algebraic equations, number theory and geometry.
		Galois is honored as the first mathematician linking group theory and field theory, with the theory is now called Galois theory.
		The study of what are now called Lie groups, and their discrete subgroups, as transformation groups, started systematically in 1884 with Sophus Lie; followed by work of Killing, Study, Schur and Maurer.
	www.wikinfo.org /wiki.php?title=Group_theory (1093 words)

	Glossary of group theory
		A group is a set together with an associative operation such that every element has an inverse.
		Given a group G and a normal subgroup N of G, the quotient group is the set G/N of left cosets {aN : a∈G} together with the operation aN*bN=abN.
		As a result of extensive effort ove the second half of the 20th century, the finite simple groups have all been classified.
	publicliterature.org /en/wikipedia/g/gl/glossary_of_group_theory.html (848 words)

	Number Theory Glossary (Site not responding. Last check: 2007-10-16)
		An abelian group is a group whose operation is commutative, ie
		An example of a group which is not abelian is the rotations of a cube (try it out).
		When dealing with an abelian group is it conventional to denote the group operation as addition (+), rather than multiplication (*) and to denote the unit element as 0 rather than 1.
	www.math.umbc.edu /~campbell/NumbThy/Class/Glossary.html (827 words)

	Great American Insurance Group - Insurance Glossary (Site not responding. Last check: 2007-10-16)
		Single policy under which individuals in a natural group (such as employees of a business firm) and their dependents are covered.
		Group of insurers or reinsurers involved in joint underwriting.
		The portfolio typically is a group of mutual funds established by the insurer as a separate account, with the policyholder given some investment discretion in choosing the mix of assets among, say, a common stock fund, a bond fund, and a money market fund.
	www.greatamericaninsurance.com /pages/gai_insuranceGlossary.jsp (7600 words)

	Web Glossary -- Recommendations and Resources (Site not responding. Last check: 2007-10-16)
		This is a glossary of some terms used in the branch of mathematics known as topology.
		It seems that the current glossary is evolving into a "general topology" glossary (i.e.
		The word ''glossary'' itself is derived from the Greek ''glossa'' (γλωσσα) meaning "tongue".
	www.becomingapediatrician.com /health/167/web-glossary.html (906 words)

	Set Theory Glossary
		Those that apply to harmonic theory are listed with an [h] and those that apply to serial theory are listed with an [s].
		Hexadecimal notation in set theory provides a compact single digit system for representing pc sets; e.g., 2, 5, 7, 9, 11 in hexidecimal is 2579B, which is more concise and does not need separators.
		In set theory the word "interval" is often informally used to mean interval class, the latter of which is of greater generality.
	solomonsmusic.net /setgloss.htm (3865 words)

	Glossary
		The theory was that one factor causing Alzheimer's disease might be accumulation of excess amounts of disease-related proteins in the CSF.
		A group of people or animals that does not receive a treatment or other intervention or that is not affected with the disease being studied.
		This group is used as a standard to compare any changes in a group that receives treatment or has the disease.
	www.alz.org /Resources/Glossary.asp (4880 words)

	SFB 504 glossary: Game theory
		Game theory provides general methods of dealing with interactive optimization problems; its methods and concepts, particularly the notion of strategy and strategic equilibrium find a vast number of applications throughout social sciences (including biology).
		Based on a model of optimizing agents that plan individually optimal course of play, knowing that her opponents will do so as well, the basic objects of interest in strategic (or 'non-cooperative') game theory are the players' strategies.
		In addition to the strategic branch of game theory, there is another one that focuses on the interactions of groups of players that jointly strive to maximize their surplus.
	www.sfb504.uni-mannheim.de /glossary/game.htm (1533 words)

	RPG Theory Glossary Entries: S
		In narrative theory terms, this is the circumstances of the main characters of a narrative.
		Within GNS theory, the sum of all interactions and relationships among members of the role-playing group.
		In GNS theory, what stands to be lost and/or gained during Gamist play; the term may be applied at either or both Step on Up or Challenge levels of play.
	www.darkshire.net /~jhkim/rpg/theory/glossary/alphabetical/S.html (799 words)

	Decision Modeling
		Progress was made two centuries later when John von Neumann and Oskar Morgenstern published Theory of Games and Economic Behavior (1944).
		Utility Theory - University of Colorado at Boulder - Psychology
		Ernst Zermelo is credited with game theory's first theorem (1913) by showing that a solution algorithm for chess exists (even though it is not computable in practice).
	groups.msn.com /DecisionModeling/utilitytheory.msnw (903 words)

	Interest group: A Glossary of Political Economy Terms - Dr. Paul M. Johnson
		Interest groups typically have formal admission to membership, dues, elected officers, by-laws and regular meetings, and they often provide information and regular opportunities for communication through newsletters or magazines, sponsor recreational or educational activities, organize volunteer public service projects, make deals for group discounts or group insurance and so on.
		Many interest groups at least occasionally engage in some form of lobbying or other political activities with respect to issues that touch directly on the common interests that are the organization's reason for being -- for example, the PTA may organize support for a bond issue election to pay for erecting a new school building.
		Interest groups that exist primarily for exerting political influence as a means of affecting government policies or legislation are often referred to by the narrower term pressure groups.
	www.auburn.edu /~johnspm/gloss/interest_group (242 words)

	Synthetic Theory of Evolution: Glossary of Terms
		the relatively rapid expansion and diversification of an evolving group of organisms as they adapt to new ecological niches.
		The Old Order Amish are a relatively closed group that shun most modern conveniences in their farming lifestyle.
		This is essentially a combination of Darwin's concept of natural selection, Mendel's basic genetics, along with the facts and theories of population genetics and molecular biology.
	anthro.palomar.edu /synthetic/glossary.htm (4294 words)

	SUPERSTRINGS! Glossary
		This refers to the situation where the strong coupling limit of one theory is described by a different theory at weak coupling.
		When both theories are at weak coupling they may look very different, however when one is at strong coupling and the other at weak coupling they describe exactly the same physics.
		Therefore when one of the theories is on a very small circle the other theory is on a very large circle.
	www.sukidog.com /jpierre/strings/glossary.htm (930 words)

	SCI Coverage Matrix Glossary: Group Purchasing Arrangements
		Group purchasing arrangements (GPA) are public or private efforts to allow more than one small or large employer and/or individuals to pool together to collectively purchase health insurance.
		On January 1, 2005, the first health insurance purchasing group in Arkansas was initiated.
		PEIA is the largest self-insured plan in the state, providing insurance to public employees in state agencies, state universities, and colleges, as well as county boards of education.
	www.statecoverage.net /matrix/grouppurchasing.htm (1341 words)

	Superconductor Terms
		The theory asserts that, as electrons pass through a crystal lattice, the lattice deforms inward towards the electrons generating sound packets known as "phonons".
		A class of molybdenum chalcogenides (compounds containing Group VI elements S, Se or Te along with molybdenum and a positively charged metal ion) - named for Roger Chevrel of the University of Rennes, whose research brought them to the attention of the scientific community in the early 1970's.
		Since electron-pairing is universally agreed to be the method by which superconductivity occurs, this is the amount of energy required to disrupt the superconducting state.
	superconductors.org /terms.htm (4425 words)

	Dictionary for the Study of the Works of Michel Foucault
		An episteme is researched through the analysis of discourse (text), but there are practices (institutions, architectural arrangments, regulations, laws, administrative measures, scientific statements, philosphic propositions, morality, philanthropy) in addition to discourse which we may use to do a genealogical analysis of some particular situation (Dreyfus and Rabinow, p.121).
		The genealogy of knowledge consists of two separate bodies of knowledge: First, the dissenting opinions and theories that did not become the established and widely recognized and, second, the local beliefs and understandings (think of what nurses know about medicine that does not achieve power and general recognition).
		The genealogy is concerned with bringing these two knowledges, and their struggles to pass themselves on to others, out into the light of the day.
	www.california.com /~rathbone/foucau10.htm (4087 words)

	RUMEC APOS Theory Glossary
		Given a specific group with a binary operation algorithm one can apply, a specific subgroup and a specific element, an action is to calculate the elements of the left coset containing that element.
		Understanding a coset in group theory only as a set of calculations that are actually performed to obtain a definite set is an action conception.
		In abstract algebra a student has a trans level of development for a group schema when the student is guided by the definition or relevant theorems in determining whether a certain subset of an abstract group is also a group under the same binary operation.
	www.cs.gsu.edu /~rumec/Papers/glossary.html (3991 words)

	Integrity Mortgage Group \| Glossary
		LIEN THEORY: A concept followed in several states, including Florida, providing that a mortgage represents a lien on the property with the mortgagor retaining legal title.
		LIS PENDEDS: A notice recorded in the official records of a county to indicate there is a pending suit affecting property in that jurisdiction; notice of intent to file foreclosure proceeding or to place a lien on the property.
		TITLE THEORY: A concept used in some states providing that the mortgagee holds legal title to the property, as opposed to holding a lien against the property.
	www.imgfl.com /glossary.htm (5065 words)

	Color Wheel Pro: Color Theory Basics
		According to color theory, harmonious color combinations use any two colors opposite each other on the color wheel, any three colors equally spaced around the color wheel forming a triangle, or any four colors forming a rectangle (actually, two pairs of colors opposite each other).
		He divided all the colors into two groups – the plus side (from red through orange to yellow) and the minus side (from green through violet to blue).
		The current form of color theory was developed by Johannes Itten, a Swiss color and art theorist who was teaching at the School of Applied Arts in Weimar, Germany.
	www.color-wheel-pro.com /color-theory-basics.html (676 words)

	Music Terms Glossary - Music Theory Lessons
		Throughout the course we will be using many terms that you may or may not know already.
		key - A key is a group of notes and chords built on the notes of a scale, centered on the root.
		mode - If theory is learned properly, the meaning of this would be different, but this term generally applies to a group of seven note scales.
	www.theorylessons.com /terms.html (674 words)

	Encyclopaedia of Design Theory: Glossary (Site not responding. Last check: 2007-10-16)
		A permutation group on a set X is a group whose elements are permutations of X and whose operation is composition of permutations.
		A permutation group is said to be primitive if there is no partition of the domain which is preserved by the group apart from the trivial partitions (the partition into singletons, and the partition with just one part).
		The rank of a permutation group is equal to the number of orbits of the group on the set of ordered pairs of points; in other words, the number of basis matrices for the group.
	designtheory.org /library/encyc/glossary (13994 words)

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