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Topic: Index of a subgroup

	PlanetMath: core of a subgroup
		, as the core of the subgroup is trivial.
		It also follows that a group is virtually abelian if and only if it is abelian-by-finite, because the core of an abelian subgroup of finite index is a normal abelian subgroup of finite index (and the same argument applies if `abelian' is replaced by any other property that is inherited by subgroups).
		This is version 7 of core of a subgroup, born on 2005-12-30, modified 2007-06-13.
	www.planetmath.org /encyclopedia/CoreOfASubgroup.html (155 words)

	PlanetMath: calculus of subgroup orders
		We further inforce a policy of drawing edges of the same length if the index of the corresponding subgroups are equal.
		It is also quite common to prove certain configurations of subgroups are impossible as the indices are relatively prime.
		This is version 5 of calculus of subgroup orders, born on 2006-03-24, modified 2006-07-24.
	www.planetmath.org /encyclopedia/TheoremOfLagrange.html (487 words)

	Oberlin College Archives \| Finding Guides \| RG 5 - Office of the Secretary \| Scope and Content
		The master index, a comprehensive record of names from the founding of the college in 1833 was prepared between 1906 and 1979.
		Less general than subgroup I, the records in subgroup II consist of records of the academic departments and programs, administrative offices and units, and annual reports submitted to the Office of the Secretary by department heads.
		Subgroup VI is made up of records representing the functional duties of the secretary in regard to organizing special events such as centennials, presidential inaugurations, and annual events like commencement.
	www.oberlin.edu /archive/holdings/finding/RG5/scope.html (4845 words)

	Output Data Sets
		A subgroup standard deviation variable is included if you specify the STDDEVIATIONS option; otherwise, a subgroup range variable is included.
		Subgroup summary variables are created for each process specified in the XCHART statement.
		For example, if you request all eight tests and Tests 2 and 8 are positive for a given subgroup, the value of _TESTS_ has a 2 for the second character, an 8 for the eighth character, and blanks for the other six characters.
	www.asu.edu /it/fyi/dst/helpdocs/statistics/sas/sasdoc/sashtml/qc/chap42/sect12.htm (597 words)

	Index - Wikinfo
		Indexing skills have also been applied to periodicals and databases, and web indexing is now becoming important.
		In mathematics, an index (plural 'ndices) is a superscript or subscript to a symbol.
		The index of a subgroup is the number of its left cosets (which is equal to the number of its right cosets).
	www.wikinfo.org /wiki.php?title=Index (721 words)

	How to obtain the index of group-subgroup relation
		As consequence a maximal subgroup is always or t-subgroup or k-subgroup of the initial group.
		is the k-index (the klassengleich index), which coincides with the cell multiplication in the subgroup in the case of primitive cells, and i
		The index of a transformation is related with the number of formula units of the two structures whose symmetry groups are group-subgroup related.
	www.cryst.ehu.es /cryst/help/index.html (657 words)

	College of American Pathologists - Genes pointing the way in lymphoma prognosis
		Patients in the type 3 subgroup had a survival rate of 39 percent; those in the activated B-cell-like subgroup had the poorest prognosis, with a survival rate of 35 percent.
		As with the three original subgroups, the cell of tumor origin was found to predict survival.
		The international prognostic index, which commonly has been used to predict outcome, measures such parameters as patient age, stage of disease upon diagnosis, total tumor bulk as measured by serum lactate dehydrogenase, performance status of patient upon diagnosis, and whether the tumor has spread beyond the lymph nodes.
	www.cap.org /apps/cap.portal?_nfpb=true&cntvwrPtlt_actionOverride=%2Fportlets%2FcontentViewer%2Fshow&_windowLabel=cntvwrPtlt&cntvwrPtlt%7BactionForm.contentReference%7D=cap_today%2Ffeature_stories%2Flymphoma_prognosis.html&_state=maximized&_pageLabel=cntvwr (1680 words)

	Subgroups of Finite Index
		The conjugacy classes of subgroups are returned in the form of a sequence of sets of words, where the i-th set is a generating set for a representative subgroup from the i-th conjugacy class of subgroups satisfying the given conditions.
		Given subgroups H and K, both of finite index in the fp-group G, return an indexed set of words which comprise a set of representatives for the double cosets HuK of H and K in G, as well as a map from G to the representatives.
		We define a subgroup as the core of one of the subgroups of index 7.
	www.math.lsu.edu /magma/text427.htm (3812 words)

	Washington County, Tennessee, Court Records
		Subgroup C contains the administrative records of the clerk of chancery court and legal documents submitted to or generated by the chancery court concerned with the settlement of estates, divorces, damages, debts, and delinquent taxes.
		Subgroup D contains administrative records and legal documents generated by or submitted to the county court which functioned as a judicial body, financial administrator, and supervisor of public education and elections in Washington County.
		This subgroup includes exhibits to unidentified cases as daybooks, account books and ledgers; bound volumes of the juvenile court and the jury commission; correspondence; property descriptions; ballads; and legal documents of which the court could not be ascertained.
	www.rootsweb.com /~tnwashin/documents/washcort.htm (2380 words)

	Index (Site not responding. Last check: )
		Indexing skills have also been applied to periodicals and databases, and web indexing is now becoming important.
		The index of a Fredholm operator is the dimension of its kernel minus the dimension of its cokernel.
		The index of a real quadratic form Q is defined (but not always consistently) as p\ − q where Q can be written as a difference of p squared linear terms and qsquared linear terms.
	www.billmanrealestate.com /index.html (244 words)

	Low Index Subgroups
		The conjugacy classes of subgroups are returned in the form of a sequence of sets of words, where the i-th set is a generating set for a representative subgroup from the i-th conjugacy class of subgroups satisfying the given conditions.
		Subgroup class 6 Index 14 Length 7 Subgroup generators :- { a, b^-1 * a * b * a * b^-1 * a * b * a * b^-1 * a * b * a * b^-1 * a * b, b * a * b * a * b^-1 }
		Subgroup class 8 Index 14 Length 7 Subgroup generators :- { a, b * a * b * a * b^-1 * a * b^-1 * a * b * a * b * a * b^-1 * a * b^-1, b^-1 * a * b * a * b }
	www.math.ufl.edu /help/magma/text235.html (1972 words)

	PlanetMath: Sylow theorems, proof of
		Proposition 3 The intersection of a Sylow p-subgroup with the normalizer of a Sylow p-subgroup is the intersection of the subgroups.
		Cross-references: factor, sum, congruent, stabilizer, index, orbit-stabilizer theorem, action, subset, orbits, group action, conjugation, act on, conjugates, remainder, multiple, second isomorphism theorem, addition, Sylow p-subgroups, normalizer, intersection, divisible, proposition, normal, subgroup, generated by, cyclic subgroup, Cauchy's theorem, induction, Sylow p-subgroup, equation, right, side, class equation, center, conjugacy class, size, divides, Sylow's theorems, order, group
		This is version 9 of proof of Sylow theorems, born on 2002-07-22, modified 2006-08-13.
	planetmath.org /encyclopedia/ProofOfSylowTheorems.html (462 words)

	PlanetMath: order of a profinite group (Site not responding. Last check: )
		In particular, we can define the order of a profinite group to be the index of the identity subgroup in
		index of a profinite subgroup, index of a profinite group
		This is version 2 of order of a profinite group, born on 2005-07-15, modified 2005-07-15.
	planetmath.org /encyclopedia/IndexOfAProfiniteGroup.html (162 words)

	Lie group Summary
		The group U(1)×SU(2)×SU(3) is a Lie group of dimension 1+3+8=12 that is the gauge group of the standard model, whose dimension corresponds to the 1 photon + 3 vector bosons + 8 gluons of the standard model.
		Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
		The subgroup of G generated by N is the identity component of G.
	www.bookrags.com /Lie_group (4005 words)

	1350.0 - Australian Economic Indicators, Jun 2001
		The item coverage of living cost indexes is determined by reference to all those amounts actually paid by households to gain access to consumer goods and services, while the item coverage of inflation indexes is defined as all those goods and services actually acquired by households in monetary transactions.
		The index series for the various population subgroups from June quarter 1998 to June quarter 2000 are shown in chart 1 and quarterly percentage changes in the indexes in chart 2.
		Between the December quarters 1999 and 2000 the increases in the population subgroup indexes ranged from 5.6% for Self-funded retiree households to 6.6% for Employee households.
	www.abs.gov.au /AUSSTATS/abs@.nsf/Previousproducts/1350.0Feature%20Article360Jun%202001?opendocument&tabname=Summary&prodno=1350.0&issue=Jun%202001&num=&view= (2831 words)

	Explanatory Notes for 1999-00 API Growth Report - Academic Performance Index (CA Dept of Education)
		The PSAA defines a "numerically significant ethnic or socioeconomically disadvantaged subgroup" as a subgroup "that constitutes at least 15 percent of a school's total pupil population and consists of at least 30 pupils." Also, in light of the sizable enrollments at many California schools, the State Board of Education has adopted an additional criterion.
		If a subgroup defined by ethnicity or socioeconomic disadvantage constitutes at least 100 pupils, i.e., at least 100 pupils with valid STAR scores, that subgroup is "numerically significant" and required to demonstrate comparable improvement, even if it does not constitute 15 percent of the school population.
		For subgroups within schools with schoolwide APIs between 781 and 799, i.e., approaching the statewide interim performance target of 800, the annual growth target was one point.
	www.cde.ca.gov /ta/ac/ap/expnotes99g.asp (2254 words)

	Interactive Coset Enumeration
		Since the index of the chosen subgroup is 1 140 000, we request a coset limit of 1 200 000.
		Finally, we are interested in the quotient of G by the normal closure of the subgroup generated by a^4 and want to enumerate the cosets of the image of the subgroup generated by a^2 in this quotient.
		Given a finite index subgroup H of a group G, the action of G on the set of right cosets of H in G by right multiplication defines a permutation representation rho : G -> S of G onto a suitable subgroup S of the symmetric group on [G:H] letters.
	www.umich.edu /~gpcc/scs/magma/text471.htm (5151 words)

	Magnus
		In order to see if an element is in a subgroup, we add the generators of the subgroup to the defining relations of the containing group and then check to see if the image of the given element is trivial in the resultant group.
		The index of the given subgroup in the overgroup is the order of the factor group of the overgroup by the subgroup.
		The isolator of a given subgroup is the pre-image of the torsion subgroup of the factor group of the given group by the subgroup.
	zebra.sci.ccny.cuny.edu /web/caiss/MAGNUS/website/pages/checkinabeliangroup.html (1968 words)

	Monoids and Groups. Group Theory and Symmetries - Numericana
		A proper subgroup of G is a subgroup of G not equal to it.
		G itself and the trivial subgroup {e} are normal subgroups of G, The derived subgroup G' is also always a normal subgroup of G. The center of a group consists of the elements which commute with every element of the group (such elements are said to be central).
		For any subset E of the group G, the subgroup generated by all the conjugates of the elements ofnbsp; E is called conjugate closure of E. It's a normal subgroup containing E. In fact, it's the smallest normal subgroup containing E (i.e, it's the intersection of all normal subgroups containing E).
	home.att.net /~numericana/answer/groups.htm (5201 words)

	CHROMATIC PLANE COMPOSITIONS
		The main theorem of the article is the Theorem 2 which by means of the color equation characterizes the successions of subgroups of a crystallographic group which may be the isotropy color groups of a chromatic plane periodic composition.
		The main theorem of the article is the theorem which by means of the color equation characterizes the successions of subgroups of a crystallographic group which may be the isotropy color groups of a chromatic plane periodic composition.
		From the table of subgroups of the crystallographic plane groups [1] and if we take into account that the subgroup pmm must be counted twice, the number of dichochromatic plane groups is 46.
	www.mi.sanu.ac.yu /vismath/ruiz1/index.html (3705 words)

	[No title]
		Since H is not normal, the number of 2-sylow subgroups is greater than or equal to 3.
		But since the index of P in H1 and H2 is 2, P is normal in H1 and H2.
		The index of M in G is 2, so M is normal in G. ¡d§PPgPÃPåçÿçÿ"-çÿçÿ,çÿçÿçÿçÿçÿçÿêó ¨ Subcase 1¨_H is isomorphic to Z8 Since H is cyclic, it can be generated by some element p in G, so H= Then P= is isomorphic to Z4.
	www.uwec.edu /Math/papers/2006_ElgindiTM-A_Classification_of_Groups_of_Order_24.ppt (994 words)

	Technical Notes on the Wholesale Price Index (WPI)
		The index is a vital guide in economic analysis and policy formulation, and as basis for price adjustments in business contracts and projects.
		The index for the next subgroup of commodities is computed by dividing the aggregate of weighted indices of component items in a subgroup by the total of their corresponding weights, as follows:
		The weighted average of these subgroup indexes, in turn, becomes the index of the major commodity group, until finally the weighted average of the major commodity group indexes becomes the overall index.
	www.census.gov.ph /data/technotes/notewpi.html (1118 words)

	Workplace Consultants, Inc. - Storm Index Report
		Via this analysis the STORM Index report identifies the major values and assumptions that are shared by the workforce and determine how effective the culture is in supporting corporate goals and objectives.
		Through the STORM Index it was found that workers, although highly stressed, actually sought after and created stress in their workplace because that is what they wanted to help them perform.
		The STORM Index identified a conflict between the cultural values of the company and the way the company had structured itself in terms of effort and reward.
	www.stormindex.com /report.html (826 words)

	Archived: Growth Models: Flexibility and Accountability
		This New Path "equation" includes the primary elements of the law, such as annual testing and reporting of subgroup data, plus increasing student achievement and a narrowing of the achievement gap, plus overall sound state education policies that ensure that progress is being made.
		States that show results and follow the requirements of NCLB are eligible for new tools to help them meet the law's goals of getting every child to grade level by 2014.
		For States that cannot track individual student progress, an index model provides an alternative that gives schools credit for moving students from "below basic" to "basic" even if they are not yet proficient.
	www.ed.gov /admins/lead/account/growthmodel/factsheet.html (643 words)

	[No title]
		Subgroups In this lecture we want to go over operations related to subgroups.
		As an example, let's find the Sylow subgroups of S_4 / G := Sym(4); H := SylowSubgroup(G,3); H; / We can see that H is the alternating group on 3 of the four elements.
		This function gives representatives for the right cosets of a subgroup (together with a function associating an element of the group to its coset).
	www.math.bgu.ac.il /~bessera/magma/lecture3 (616 words)

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