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Topic: Generating set of a group

	Generating set of a group - Wikipedia, the free encyclopedia
		In abstract algebra, a generating set of a group G is a subset S such that every element of G can be expressed as the product of finitely many elements of S and their inverses.
		More generally, if S is a subset of a group G, then , the subgroup generated by S, is the smallest subgroup of G containing every element of S; equivalently, ~~is the subgroup of all elements of G that can be expressed as the finite product of elements in S and their inverses.~~
		Every group generated by S is isomorphic to a factor group of this group, a feature which is utilized in the expression of a group's presentation.
	en.wikipedia.org /wiki/Generating_set_of_a_group (554 words)

	Generating set - Wikipedia, the free encyclopedia
		Generating set of a group: S is a generating set of a group if the smallest subgroup of G containing S is G itself.
		For example, polynomials are a generating set of the space of all continuous functions on the closed unit interval, because taking closure under limits forms the entire space.
		In linear algebra, S is a generating set or spanning set of a vector space V if V is the linear span of S.
	en.wikipedia.org /wiki/Generating_set (139 words)

	Finitely Presented Groups [HB 20, 21]
		Coercion of elements of a finitely presented group into a subgroup defined by a set of generating words is now possible to some limited extent.
		The group returned is created as a subgroup of the original group, which allows coercing elements from the original group into the new group.
		It is particularly useful for eliminating redundant generators in subgroups of finitely presented groups obtained as preimages under a homomorphism.
	www.math.niu.edu /help/math/magmahelp/rel/node9.html (704 words)

	Generator article - Generator electrical generator generating of group computer science Python - What-Means.com (Site not responding. Last check: 2007-11-07)
		In computer science, particularly in the Python programming language, a generator is a type of continuation that can be used as an iterator.
		This is a disambiguation page; that is, one that points to other pages that might otherwise have the same name.
		Generator article - Generator definition - what means Generator
	www.what-means.com /encyclopedia/Generator (102 words)

	Generators and fundamental regions
		A generating set for the symmetry group of a plane pattern P is a set S of symmetries of the pattern such that every symmetry of the pattern is a product of transformations which are either elements of S or inverses of elements of S.
		In Kaleidomania one particular generating set is chosen for each type of plane symmetry group.
		The set of generators chosen by by Kaleidomania for this pattern is {T, V
	www.math.uga.edu /~clint/2005/5210/gens.htm (508 words)

	Automorphisms and Isomorphisms (Site not responding. Last check: 2007-11-07)
		A PAG-generating sequence for a soluble group is a generating sequence which ascends the group via a polycyclic series with prime factors.
		A generating set for a supplement to the inner automorphism group is returned as a sequence of homomorphisms; each describes the action of a generator of the automorphism group on the generators of the group.
		The function returns a generating set for a supplement to the inner automorphism group of G. This generating set is returned as a sequence of homomorphisms, where each describes the action of an automorphism on the generators of G. [Next] [Prev] [Right] [Left] [Up] [Index] [Root]
	www.math.uga.edu /~matthews/DOCS/MAGMA/text278.html (1524 words)

	element - Wiktionary
		(set theory) One of the objects in a set.
		A group of people within a larger group having a particular common characteristic.
		A component in electrical equipment, often in the form of a coil, having a high resistance, thereby generating heat when a current is passed through it.
	en.wiktionary.org /wiki/element (322 words)

	Base and Strong Generating Set
		Set the base of G to be [B[1],..., B[n]] where the tuple B has n components.
		Set the limit for the size of the first basic orbit to be n.
		Given a matrix group G for which a base and strong generating set are known, and an integer i, where 1 <= i <= k with k the length of the base, return the subgroup of G which fixes the first i - 1 points of the base.
	www.math.lsu.edu /magma/text306.htm (1235 words)

	Group Policy Administrative Tools: Group Policy (Site not responding. Last check: 2007-11-07)
		The Resultant Set of Policy snap-in is an MMC used to determine which policy settings are in effect for a given User or Computer, or to predict the effect of applied policy.
		Group Policy Object Editor is an MMC snap-in used to edit the policy settings in Group Policy objects (GPOs).
		Resultant Set of Policy (RSoP) snap-in is an MMC used to predict the effect of GPOs on the network as a whole, or to determine the effect Group Policy has had on a specific user or computer.
	www.microsoft.com /technet/prodtechnol/windowsserver2003/library/TechRef/abc2890d-f3f1-408c-bafc-ac9e4e5b0e83.mspx (1643 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		A generating set of the symmetric group is > a set of permutations where every element of the symmetric group can be > generated as a product of the elements of the generating set.
		> > Another way of saying this is "Are the necessary and sufficient > conditions for a set of 3 permutations of length n to generate Sn known?" > In the 1960s Sims developed an algorithm for replacing a set of generators of a subgroup of S_n by a set of strong generators.
		Given a subset A of S_n, this subset generates a subgroup of S_n, namely is the set of all products of elements of A. I won't say what a set of strong generators is, except to say that if one has such a set, then one can read off the order of immediately.
	www.math.niu.edu /~rusin/known-math/98/sims (526 words)

	NIK RUSKUC: ABSTRACTS (Site not responding. Last check: 2007-11-07)
		To each element s\in S we associate a permutation group G_R(s) acting on the image of s, and we find a natural generating set for this group.
		By a certain duality process we associate to s another permutation group G_L(s) on the image of s, and prove analogous results for the L-class of s.
		Finally we prove that the Schutzenberger group of the H-class of s is isomorphic to the intersection of G_R(s) and G_L(s).
	www-groups.dcs.st-and.ac.uk /~nik/Abstracts/genschgp.html (170 words)

	Facilitating a Group Problem-Solving Meeting
		As meeting facilitators, you will set the meeting’s agenda, guide the class through this agenda, and work with the class to develop and select the best solution to your case’s problem.
		Any case your group locates/creates must be approved by your instructor at least one week prior to your scheduled presentation date.
		If your group facilitates for less than the 18 minutes, or more than 23, your group grade will be penalized.
	www.utexas.edu /courses/spe319/assignments/Group.html (696 words)

	OUTSTANDING PROBLEMS (Site not responding. Last check: 2007-11-07)
		Let F = F_n be the free group of a finite rank n with a fixed set X = {x_1,...,x_n} of free generators.
		Of particular interest are n=5, n=8, n=9 and n=12 - values for which, by the experts' opinion, groups of exponent n have a remote chance of being locally finite.
		Is the automorphism group of a free group of rank 2 linear?
	www.cs.gc.cuny.edu /~cryptlab/gworld/problems/probout.html (334 words)

	Calculation of the cross ratio (Site not responding. Last check: 2007-11-07)
		For example, Fuchsian groups consist of a set of linear transformations acting on the unit disk generating a discrete group [2].
		In general, the curve in equation 3 is a polynomial of degree 8.
		are chosen from the generating set of the group.
	www.csc.fi /math_topics/DH/node7.html (552 words)

	Frattini (Site not responding. Last check: 2007-11-07)
		The route that Frattini had taken to undertake research in group theory had been to study Camille Jordan's papers on the topic.
		These are not two of the three papers which have made him famous, the latter being three papers on the generators of finite groups one of which he published in 1885 and the remaining two in 1886.
		His definition was as the subgroup generated by all the non-generators of the group (elements which if included in a generating set for the group can always be omitted to still leave a generating set).
	www-history.mcs.st-and.ac.uk /history/Mathematicians/Frattini.html (905 words)

	Independent generating sets and geometries for symmetric groups (Site not responding. Last check: 2007-11-07)
		Julius Whiston showed that the size of an independent generating set in the symmetric group $S_n$ is at most $n-1$.
		We also give some general remarks on the maximum size of an independent generating set of a group and its relationship to coset geometries for the group.
		In particular, we determine all coset geometries of maximum rank for the symmetric group $S_n$ for $n>6$.
	student.vub.ac.be /~pcara/download/ABSTRACTigsgsn.html (80 words)

	Generating sets
		It is also generated by the reflection about the vertical and the reflection about the horizontal.
		The integers for example is finitely generated whereas the rational numbers under addition is not finitely generated.
		By convention, if X is the empty set then the (sub)group it generates is the trivial group.
	www.math.csusb.edu /notes/advanced/algebra/gp/node12.html (220 words)

	Young Characters on Coxeter Basis Elements of Iwahori-Hecke Algebras and a Murnaghan-Nakayama Formula. - Pfeiffer ... (Site not responding. Last check: 2007-11-07)
		Let W be a finite Weyl group with generating set S ae W of simple reflections.
		Denote by H the generic Iwahori--Hecke algebra associated to W with parameters q s, s 2 S. This is an associative A--algebra with basis Tw, w 2 W, and multiplication defined by TwT w = T ww if l(ww) = l(w) + l(w); s = q s T 1 + (q s...
		Group Actions on Arrangements of Linear Subspaces and..
	citeseer.ist.psu.edu /pfeiffer94young.html (576 words)

	generating set
		There is always a generating set that corresponds to the power, frequency and voltage of your requirements The most important brands of engines install our generator sets.
		To this generating set him the released thermal energy through the combustion can be taken advantage of gases, by means of installed heat exchangers in the circuits of refrigeration of shirts, of lubricating oil, plus an extra advantage in a boiler of exhaust gases recovery.
		Study of an absorption refrigerating machine using the residual heat of a generating set as energy source.
	generating-set.trabajosenespana.com (478 words)

	GAP Manual: 26 Special Ag Groups
		For a nilpotent group N, the group lambda_2(N) = lambda_2(P_1) cdots lambda_2(P_l) is the Frattini subgroup of N.
		But be careful, because the output H is not handled as a special ag group by GAP but as an arbitrary ag Ag Group Functions for Special Ag Groups use the algorithms for special ag groups.
		If you call one of these general functions with an arbitrary ag group, the general function will not calculate the special ag group but use the function for ag groups.
	parallel.rz.uni-mannheim.de /gap/htm/CHAP026.htm (1749 words)

	TVinsite \| Cahners In-Stat Group
		The set top box market has sputtered this year, but Internet access and other features are making set tops more versatile and more attractive to providers and subscribers.
		Internet access via set top boxes is still a relatively new feature with manufacturers in each of the five segments trying to find the best combination of hardware and software to appeal to consumers.
		This research highlight is drawn from the Cahners In-Stat Group report, Set Top Box Internet Access: Planting Seeds for a Walled Garden (#ID0106AD), which gives arguments for both the “full” or limited access via a “walled garden” approaches to accessing the Internet, as well as insight into trends affecting each segment.
	www.instat.com /rh/tvinsite/rh_id0106ad.asp (676 words)

	Introductory Transact-SQL
		Since SQL is a set-oriented query language, statements that group or summarize data are its bread and butter.
		Generating summary information by looping through a table is a common technique in older database products—but not in SQL Server.
		Its relationship to GROUP BY is similar to the relationship between the WHERE clause and the SELECT itself.
	www.developer.com /db/print.php/10920_2202631_8 (600 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		In terms of possible worlds, S4 is the logic of a set of possible worlds such that the accessibility relationship among the worlds is reflexive and transitive.
		In terms of possible worlds, S5 is the logic of a set of possible worlds such that the accessibility relationship among the worlds is reflexive,symmetric and transitive.
		A special case of interest is Cayley graphs that have as their generating set a permutation group.
	www.andrew.cmu.edu /user/rramyaa/research.doc (1149 words)

	VBM 4.0 Tutorial
		Setting up payee groups is another way to make your bill paying even easier.
		For example, you may want to set up a group for all your bills due on the first of each month and call this group First of the Month.
		Select the payees you want to include in the group and enter the name in the Group Name field at the bottom of the screen.
	www.bankofamerica.com /military/testdrive/htm/vbm4_tut_38.html (147 words)

	Base and Strong Generating Set
		For matrix groups of small degree, we use an analogue of the methods used for permutation groups.
		Thus, we have a concept of a base and strong generating set (BSGS) similar to that employed in the case of permutation groups.
		Once such a BSGS is available, analogues of the permutation group backtrack searches for centralizer, normalizer etc may be described.
	magma.maths.usyd.edu.au /magma/Features/node26.html (104 words)

	Set-Theoretic Operations in a Group
		The index of the subgroup H in the group G, returned as an ordinary integer.
		Create a process to generate pseudo-randomly chosen elements from the group G. The process uses an `expansion' procedure to construct a set of elements corresponding to fairly long words in the generators of G [CLGM+95].
		An element, pseudo-randomly chosen, from the group G. An exponent vector in normal form is chosen at random.
	magma.maths.usyd.edu.au /magma/htmlhelp/text448.htm (640 words)

	I3A Standards - Initiatives - DIG35 (Site not responding. Last check: 2007-11-07)
		By establishing standards, the Initiative Group seeks to overcome a variety of challenges that have arisen as the sheer volume of digital images being used has increased.
		A key decision made by the DIG35 Initiative Group was the choice of XML (Extensible Markup Language) as the recommended reference implementation structure.
		One of the ways that the DIG35 Initiative Group process is ensuring the real-world viability of its metadata recommendations is through the use a defined process of "Use-Case" Modeling.
	www.i3a.org /i_dig35.html (587 words)

	Uniform Growth, Actions on Trees and GL_2 (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Using these remarks, Milnor showed that exponential growth is independent of the generating set.
		Gromov has asked if there is a group of exponential growth which is not of uniform exponential growth.
		2 The entropy of solvable groups (context) - Osin - 2000
	citeseer.ist.psu.edu /447208.html (363 words)

	DIR - Meeting Notes for TGIC Technical Advisory Committee
		The Texas Geographic Information Council is created to provide cost-effective and useful exchange and retrieval of geographic information both within and among the various agencies and branches of government, and from the agencies and branches of state government to the people of Texas and their elected representatives.
		The last meeting set some basic goals of and is working on defining short-term (off the shelf solution) and long-term (local and online updates) milestones.
		A working group chair will be elected and meeting dates set for the rest of the year.
	www.dir.state.tx.us /tgic/committee/tac/meetings/tac-2001-05-09.htm (1228 words)

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