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Topic: Ordered group

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	PlanetMath: partially ordered group
		A po-group whose underlying poset is a lattice is called a lattice ordered group, or an l-group.
		In fact, an directed integrally closed group is an Abelian po-group.
		This is version 5 of partially ordered group, born on 2007-02-17, modified 2007-04-12.
	planetmath.org /encyclopedia/LatticeOrderedGroup2.html (287 words)

	PlanetMath: ordered group
		(with the operation denoted multiplicatively) defines an order for the group
		Cross-references: properties, order, pairwise disjoint, union, operation, group, subsemigroup
		This is version 10 of ordered group, born on 2004-12-27, modified 2007-02-18.
	planetmath.org /encyclopedia/OrderedGroup.html (98 words)

	Ordered group - Wikipedia, the free encyclopedia
		In abstract algebra, an ordered group is a group G equipped with a partial order "≤" which is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then ag ≤ bg and ga ≤ gb.
		If G and H are two ordered groups, a map from G to H is a morphism of ordered groups if it is both a group homomorphism and a monotonic function.
		Ordered groups are used in the definition of valuations of fields.
	en.wikipedia.org /wiki/Ordered_group (503 words)

	Comprehensive Metabolic Panel (Site not responding. Last check: 2007-10-22)
		The CMP is a frequently ordered panel that gives your doctor important information about the current status of your kidneys, liver, and electrolyte and acid/base balance as well as of your blood sugar and blood proteins.
		The CMP may also be ordered to monitor known conditions, such as hypertension, and to monitor patients taking specific medications for any kidney- or liver-related side effects.
		The CMP is routinely ordered as part of a blood work-up for a medical exam or yearly physical and is collected by inserting a needle into a vein in your arm.
	www.labtestsonline.org /understanding/analytes/cmp/cmp.html (536 words)

	Homeschool Diploma: graduation supplies, diplomas, announcements
		If your group is considering one of our packages, we'll be happy to send a sample diploma and cover if it is a group of ten or more.
		For example, if your group has 14 members and has ordered package B for groups with 10 to 24 graduates, a package refund is not a problem and would be handled as above.
		But if your group has ordered that same package B and has exactly ten members, we would not accept a refund because it would change the pricing for everyone else in the group.
	www.homeschooldiploma.com /groups/group_packages.php (1880 words)

	Group Node Objects
		However, unless one of the special ordered group nodes is used, the Java 3D renderer can choose to render a group node's children in whatever order it wishes (including rendering the children in parallel).
		The Group node object is a general-purpose grouping node.
		Group nodes have exactly one parent and an arbitrary number of children that are rendered in an unspecified order (or in parallel).
	java.sun.com /products/java-media/3D/forDevelopers/j3dguide/GroupNodes.doc.html (2281 words)

	Groups of Galaxies containing Messier objects
		HST observations of Cepheids in M100, together with the work of Nial R. Tanvir on the M96 group extrapolated to this cluster, indicate that the Virgo cluster is at a distance of some 60 million light-years.
		M104 is the dominating member of a small group called the M104 group or NGC 4594 group of galaxies.
		The M102 candidate NGC 5866 is the brightest member of a conspicuous group of galaxies in Draco, the NGC 5866 group, which contains (besides NGC 5866) the bright edge-on spiral NGC 5907, NGC 5879, and a lot of fainter galaxies.
	www.seds.org /messier/g-group.html (565 words)

	Springer Online Reference Works
		In the early 1950s group algebras of infinite groups were studied in the context of integer group algebras in algebraic topology, and for the investigation of the structure of groups.
		The group algebra of an ordered group is imbeddable in a skew-field (the Mal'tsev–von Neumann theorem).
		An example is the concept of the cross product of a group and a ring, which retains many properties of a group algebra.
	eom.springer.de /G/g045220.htm (579 words)

	Aggregate functions
		The exact group of rows is not determined until the query is executed and all rows are fetched.
		GROUP BY is specified, the default grouping is the entire grouping set.
		The median value is defined to be the midpoint in a group of ordered numbers - half of the values are above the median, and half of the values are below the median.
	ist.marshall.edu /ist466/groupfun.html (1705 words)

	[No title]
		These orders are signed by that authority and verified by all entities involved with the group.
		All group members have the capability to be a GC and could assume this duty upon assignment.
		This type of service is most attractive when the group initiator does not need to control group membership other than to verify that all members of the group conform to some previously agreed upon rules.
	www.ietf.org /rfc/rfc2093.txt (4493 words)

	A Chronology of the 401st Bombardment Group (H)
		The Group was commended by the Commanding General of the 94th Combat Wing for the accuracy of its bombing and its efficiency in adapting to Eighth Air Force procedures.
		The Group encountered fierce enemy aircraft resistance, in which it was supported by Colonel James Howard, a P-51 pilot, who single-handedly fought off 30 Nazi fighters, destroying four, and for which he was awarded the Congressional Medal of Honor.
		The Group was commended by the Commanding General of the 1st Air Division for being the first Group in the European Theater of Operations (ETO) to complete 100 missions within seven months.
	www.401bg.com /history/chronology.htm (1486 words)

	Re: [wsrm] CF4 detailed proposal for V1.07
		Unfortunately, the specification is not silent on whether the ordered group is immediately terminated.
		If all previous messages for the group have been received, the group is closed immediately.
		Alternatively, the group is closed when the RMP receives the last missing message in the group." [I prefer the "If...
	www.oasis-open.org /archives/wsrm/200408/msg00029.html (859 words)

	USN Combat Narrative: The Landing in the Solomons
		This group was ordered to land on the east coast of Gavutu Island at H plus 4 hours and seize that island, later pressing on to Tanambogo.
		This group was ordered to be prepared to land Combat Team B, less all reinforcing units, on Gavutu Island, at H plus 4 hours, and also to be prepared to attach Combat Team C, less all reinforcing units, to the Tulagi Group.
		This group was directed to be prepared to land detachments (principally antiaircraft units) on Beach RED and on Tulagi and Gavutu on the receipt of orders.
	www.ibiblio.org /hyperwar/USN/USN-CN-Solomons/USN-CN-Solomons-9.html (635 words)

	Ellis Park (Site not responding. Last check: 2007-10-22)
		Groups not canceling or "no shows" are responsible for 100% of the final account balance.
		If your group elects not to dine from the buffet but order from the menu, there is a $10.75 per person food and beverage minimum.
		Your group has the options of running a food tab, a drink tab, a food and beverage tab, soft drink tab, selecting one of the beverage packages, or having the individuals in your group pay for their own food and beverage orders.
	www.ellisparkracing.com /visit_the_track/group_sales (1646 words)

	The problem of verbal embeddings of ordered groups into ordered groups (Site not responding. Last check: 2007-10-22)
		Find a criterion under which for the given fully ordered group $H$ and for the given non-trivial word set $V$ there exists a group $G = G(H,V)$ with normal subgroup $\tilde H$, such that $\tilde H$ lies in $V(G)$ and is order isomorphic to $H$.
		The group $H$ is fully ordered if it is defined a transitive binary relation $<$ on $H$ such that for each $a, b \in H$ one and only one of the three alternatives: $a
		This groups are often called O-groups, but we adopt the term used by B. Neumann.
	www.stormloader.com /users/mikaelian/h_algeb2.html (195 words)

	Springer Online Reference Works
		If the order is total (respectively, partial), one speaks of a totally ordered group (respectively, a partially ordered group).
		The kernels of order homomorphisms are the convex normal subgroups (cf.
		A convex subgroup of an ordered group is open in this topology.
	eom.springer.de /o/o070120.htm (271 words)

	[No title]
		The injunction, issued November 19, orders Hale's group (and anybody who might be acting for it) to refrain from using the name "Church of the Creator," or variants such as "World Church of the Creator, "WCOTC, "COTC," or even the words "Church" and "Creator" together in the same name.
		She gave the group 30 days to provide a report in writing that sets forth the manner and form by which the World Church has complied with the injunction.
		This court order presents the World Church of the Creator with the loss of the racist brand name it so assiduously built up in recent years, and it is unclear whether Hale will voluntarily abide by the injunction.
	www.adl.org /Learn/news/WCOTC_Name.asp (400 words)

	Organizers of canceled raffle ordered to pay $100,000 \| LJWorld.com
		The group and its directors never responded to the lawsuit and are in default, Nixon said.
		Daugherty ordered the group to pay $5,525 in restitution to those who bought raffle tickets and pay $94,939 in fines and court costs.
		Earlier this year, the charity agreed to pay an undisclosed amount of cash to the winner of a $1.3 million house in the Kansas City suburb of Parkville because it had not sold enough tickets to pay for the house, or for a $200,000 Bentley automobile that was promised as part of the grand prize.
	www2.ljworld.com /news/2006/dec/21/organizers_canceled_raffle_ordered_pay_100000 (590 words)

	06: Order, lattices, ordered algebraic structures
		Ordered sets, or lattices, give a uniform structure to, for example, the set of subfields of a field.
		Linear orderings especially on infinite sets is the study of Ordinals in Set Theory; these are traditionally considered in 03: Mathematical Logic, especially 03G: Algebraic Logic.
		Ordered sets may be viewed as topological spaces; see 54: General Topology, especially 54F05: Ordered topological spaces, for more detail.
	www.math.niu.edu /~rusin/known-math/index/06-XX.html (606 words)

	Boy charged with playing 'chicken' ordered to group home
		An Alameda County judge ordered a 15-year-old boy on Tuesday to be placed in a group home on a charge of involuntary manslaughter for playing "chicken" with an Amtrak train in Hayward--only to be pushed from the tracks by a 14-year-old girl who was struck instead and killed.
		The boy, whose name is being withheld by The Chronicle because of his age, wore leg-irons during a hearing before Alameda County Superior Court Judge John True in a Hayward courtroom in the Feb. 18 death of Celadonia Jasmin Castro, known to friends and family as Jasmin.
		The judge ordered the boy to be placed in a group home or a wilderness rehabilitation program for an indeterminate amount of time.
	www.sfgate.com /cgi-bin/article.cgi?file=/chronicle/archive/2005/05/24/chicken24.DTL&type=printable (653 words)

	Republic of Texas group ordered to rescind letters (Site not responding. Last check: 2007-10-22)
		Judge Joseph Hart ordered the group to rescind letters mailed to about 175 banks, directing them to transfer all accounts held by the state, its agencies and political subdivisions to the organization.
		Hart gave the group one week to comply with the order before facing $10,000-a-day fines that will double each day until the letters are recanted.
		Hart earlier this year approved a temporary injunction against the group, ordering it to stop filing liens against property held by government entities and private people.
	www.lubbockonline.com /news/102996/republic.htm (310 words)

	Linearly ordered group - Wikipedia, the free encyclopedia
		In abstract algebra a linearly ordered or totally ordered group is an ordered group G such that the order relation "
		If a is an element of a linearly ordered group G, then the absolute value of a, denoted by
		Otto Hölder showed that every linearly ordered group satisfying an Archimedean property is isomorphic to a subgroup of the additive group of real numbers.
	en.wikipedia.org /wiki/Linearly_ordered_group (217 words)

	SignOnSanDiego.com > News > Metro -- Homeless group living in shelter of Cabrillo Bridge ejected
		SAN DIEGO – A group of homeless people living within the Cabrillo Bridge in Balboa Park was ordered out by police and park rangers late Thursday morning.
		The group had taken up shelter within the bridge, behind the bowling green, to keep out of the cold, said Daniel Willis, one of the men evicted.
		The group sat on a patch of grass near the bridge with few of their belongings.
	www.signonsandiego.com /news/metro/20070118-1454-bn18homeless.html (275 words)

	BBC NEWS \| Northern Ireland \| 'End' for loyalist terror group
		It said the decision was taken in response to the IRA move to decommission arms in September.
		Earlier a group of church and community figures said a loyalist feud between the LVF and the rival UVF was over.
		He said the group of church and community figures had been holding mediation talks "for some time".
	news.bbc.co.uk /1/hi/northern_ireland/4390812.stm (589 words)

	Ordered groups (Site not responding. Last check: 2007-10-22)
		Author: jan Taking an ordered set, like a text (in a text, the letters must keep a certain order, if they shall carry any information) I would like to find an algebraic structure so that I can "compress" it or classify it or whatever.
		I think, that it is not too improbable that there is some kind of formalized structure in many kinds of ordered sets.
		The reason I asked if and ordered group would always be cyclic is, that I assume that the morphisms on such groups should preserve order as well as group structure.
	www.newton.dep.anl.gov /newton/askasci/1995/math/MATH125.HTM (246 words)

	GeneralOrderedGroup -- the class of all ordered free commutative groups
		This is the class of free commutative groups that can be handled by the engine.
		Each object of class GeneralOrderedGroup is called a general ordered group.
		Each general ordered group is also a member of class GeneralOrderedMonoid.
	www.math.temple.edu /computing/Macaulay2/0425.html (72 words)

	Group Constructors
		All elements of the first group that are not in the second group, ordered as in the first group.
		Note that for these operations the order of processes in the output group is determined primarily by order in the first group (if possible) and then, if necessary, by order in the second group.
		The ordering of processes in newgroup is identical to the ordering in group.
	sophia.dtp.fmph.uniba.sk /mpibook/node133.html (931 words)

	Bogus Group Ordered to Pay Court Costs, Fees of Victims (Site not responding. Last check: 2007-10-22)
		The judge further ordered that anyone driving cars with “counterfeit tags” issued by the group has until September 15 to replace the tags.
		People with the bogus tags may go to Cherokee County District Court to receive an order declaring them to be the legal owner of the vehicle so they can obtain a valid title to replace the ones the leaders of the bogus group took and claim they can no longer find.
		The Cherokee Nation brought suit against Mayes’ group in August of 2000, and at that time Sewell ordered the group to stop selling the bogus tags and coins and ruled that they were fraudulently using the name of the Cherokee Nation.
	www.cherokee.org /NewsArchives/Archives2001/8-01-14.htm (394 words)

	Court orders SCO to show more code \| CNET News.com
		In consequence, she ordered the company to "provide and identify all specific lines of code that IBM is alleged to have contributed to Linux from either AIX or Dynix," IBM's two versions of Unix.
		The judge also directed SCO to "identify with specificity all lines of code in Linux that it claims rights to," repeating an order she issued in December.
		In addition, IBM was ordered to pare down a list of 7,200 potential witnesses for the trial to 1,000 of the most important prospective witnesses.
	news.com.com /2100-1014-5169444.html (743 words)

	Audit of skate group ordered - The Boston Globe
		The state attorney general's office has told the organizers of a nationally renowned synchronized skating organization in Lexington to start getting its finances audited and to turn those audits over to the state.
		In a letter to the Globe, Hanlon Rogers described her group as "a completely volunteer organization with annual elections and substantial turnover in all areas of the organization."
		She added that "several individuals, who are no longer with the organization, were unaware of the filing requirement....
	www.boston.com /news/local/articles/2007/01/18/audit_of_skate_group_ordered (603 words)

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