
	Where results make sense

Topic: Examples of groups

	PlanetMath: examples of groups
		This is the automorphism group of the given object and captures its “internal symmetries”;.
		In Galois theory, the symmetry groups of field extensions (or equivalently: the symmetry groups of solutions to polynomial equations) are the central object of study; they are called Galois groups.
		This is version 26 of examples of groups, born on 2002-06-28, modified 2006-02-25.
	planetmath.org /encyclopedia/ExamplesOfGroups.html (1002 words)

	CMBI - LHASA: Perception and Functional Groups
		For each of these groups, a pattern has been defined to describe the group; anything not matching one of the patterns is not recognized as a functional group.
		Examples of groups presently unrecognized by LHASA are thioketone, acylsilane, ketene, and sulfonamide.
		Secondly, functional groups are used to assess the effects of reaction conditions on portions of the molecule that are not supposed to react (vide infra).
	cheminf.cmbi.ru.nl /cheminf/olp/groups.shtml (532 words)

	Examples of groups
		This is an Abelian group and our first (nondiscrete) example of a Lie group: a group whose underlying set is a manifold.
		Groups are very important to describe the symmetry of objects, be they geometrical (like a tetrahedron) or algebraic (like a set of equations).
		Free groups are important in algebraic topology; the free group in two generators is also used for a proof of the Banach-Tarski paradox.
	www.fact-index.com /e/ex/examples_of_groups.html (1205 words)

	Examples of Groups
		Given a geometric figure in the plane the symmetry group of the figure consists of all isometries that transform points on the figure to points on the figure.
		This is an example of a finite group.
		The group of permutations on n objects is called the symmetric group on n objects and is symbolized by Sn.
	members.tripod.com /~dogschool/examples.html (1438 words)

	Practices in Directory Groups
		Examples include groups used to control access to stored database queries, access to web or application-server mediated processes or content, or access to network-access services, the access-control information for which is not stored in core business systems.
		Groups not being automatically maintained by directory administrators, i.e., delegated and personal groups, may eventually become unmanaged and unused and should be removed to reduce namespace overuse and to avoid potential accidental misuse.
		Groups in the group map are instances of the posixGroup objectclass, which is a static group.
	middleware.internet2.edu /dir/groups/docs/internet2-mace-dir-groups-best-practices-200210.htm (10329 words)

	An Introduction to GROUP THEORY
		For a system to be a group the binary operation (symbolized here by "•") must be valid for any pair of elements in the group and the result of the operation must be an element of the group.
		Group theory is a clear example of abstraction in modern mathematics.
		This is because in group theory commutativity is not assumed.
	members.tripod.com /~dogschool/groups.html (1440 words)

	Examples: Configuration Groups
		In this example, one group is populated with configuration data that is standard throughout the company while another group contains regional deviations from this standard.
		interfaces { t3-0/0/0 { ## ## 't3-options' was inherited from group 'northwest' ## t3-options { ## ## 'long-buildout' was inherited from group 'northwest' ## long-buildout; ## ## 'kentrox' was inherited from group 'northwest' ## compatibility-mode kentrox; ## ## 'ones' was inherited from group 'standard' ## idle-cycle-flag ones; } } }
		groups { mpls-conf { protocols { mpls { label-switched-path <-major> { retry-timer 5; bandwidth 155m; optimize-timer 60; } label-switched-path <-minor> { retry-timer 15; bandwidth 64k; optimize-timer 120; } } } } } apply-groups mpls-conf; protocols { mpls { label-switched-path metro-major { to 10.0.0.10; } label-switched-path remote-minor { to 10.0.0.20; } } } [edit] user@host#
	www.juniper.net /techpubs/software/junos/junos44/swconfig44-install/html/cli-config-groups9.html (423 words)

	20: Group Theory and Generalizations
		Group theory can be considered the study of symmetry: the collection of symmetries of some object preserving some of its structure forms a group; in some sense all groups arise this way.
		For example, the set of all curves in a topological space forms a groupoid under concatenation, that is, all the group axioms hold except a*b is not necessarily defined for all a and b.
		Nielsen's theorem: subgroups of free groups are free.
	www.math.niu.edu /~rusin/known-math/index/20-XX.html (2774 words)

	Groups, Rings, and Fields
		A consequence of the fourth property, together with the others, is that every finite group can be expressed as a set of permutations of n objects for some n, where the operation for the group is applying the second permutation to the elements of the first permutation.
		One of the simplest families of non-Abelian groups (or non-commutative groups) are the dihedral groups: these are the groups that involve both rotating a polygon with distinct corners (and thus, they have the cyclic group of addition modulo n, where n is the number of corners, as a subgroup) and also flipping it over.
		The significance of Burnside groups in general is that whether or not all groups of this kind are finite was a mathematical question only recently settled, in a paper by S. Adian and P.
	members.shaw.ca /quadibloc/math/abaint.htm (3664 words)

	Symmetries
		The set of all symmetries is a group under composition of mappings.
		Groups of symmetries of infinite figures are also of interest.
		It is possible to classify all these groups, and it turns out that there are precisely 17 of them.
	www-groups.dcs.st-and.ac.uk /~edmund/lnotes/node7.html (223 words)

	Definition and examples
		The rotations and reflections of a regular n-gon form a group where the binary operation is function composition.
		This group is known as the quaternion group and denoted by
		The symmetry group of the square is not abelian neither is the group of
	www.math.csusb.edu /notes/advanced/algebra/gp/node1.html (684 words)

	ABSTRACT ALGEBRA ON LINE: Groups
		A group G is said to be a finite group if the set G has a finite number of elements.
		Let G be a group, and let H be a subset of G. Then H is called a subgroup of G if H is itself a group, under the operation induced by G. Proposition.
		Any subgroup of the symmetric group Sym(S) on a set S is called a permutation group or group of permutations.
	www.math.niu.edu /~beachy/aaol/groups.html (1115 words)

	groups
		Examples of Infinite Groups: the integers where * = addition, the real numbers where * = addition, the positive real numbers > 0 where * = multiplication.
		Examples of Finite Groups: A = {1, -1, i, -i} where * is multiplication, B = {0, 1, 2, 3) where * is addition modulo 4.
		A subgroup is a group entirely inside another: {1, -1} is a subgroup of A, {0, 2) is is a subgroup of B.
	www.mathpuzzle.com /groups.html (581 words)

	Oracle Calendar Groups and Access Rights
		Examples of groups you might set as public: a department or the occupants of a building.
		Set groups as private that only you use, as others will not be able to view or use them.
		Examples of groups you might set as members only: a committee, a working group.
	www.itc.virginia.edu /calendar/ocgroups.html (943 words)

	Examples of Groups (Site not responding. Last check: 2007-10-20)
		The set of integers Z, is an abelian group under addition, as is the set of rational numbers (Q), real numbers (R) or complex numbers (C).
		This group is not abelian unless S has at most 2 elements.
		S. This group is called a permuatation group.
	sps.nus.edu.sg /~limchuwe/mathweb/group1_2.html (110 words)

	SparkNotes: Social Psychology: Groups
		Group cohesiveness is the strength of the liking and commitment group members have toward each other and to the group.
		When a group starts out with a dominant view that is relatively risky, the group is likely to come to a consensus that is even riskier.
		Group members are more likely to be influenced by a minority opinion when the minority holds the opinion firmly.
	www.sparknotes.com /psychology/psych101/socialpsychology/section8.rhtml (1007 words)

	MAT 310
		Group Theory is the study of symmetry in the abstract.
		In addition to understanding concrete examples of groups and their applications to the symmetries of physical objects, theorem proving will form an essential part of the course.
		Specific examples of algebraic structures are interesting -- even fascinating -- because of their connections with ideas such as symmetry.
	www.warren-wilson.edu /~teller/dept/mat_310_syl.htm (693 words)

	CMB - Non-Left-Orderable 3-Manifold Groups
		The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable.
		Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of S
		We show that several torsion free 3-manifold groups are not left-orderable.
	journals.cms.math.ca /cgi-bin/vault/view/dabkowski8386 (179 words)

	Groups of small order.
		All groups of prime order p are isomorphic to C_p, the cyclic group of order p.
		This is the same subgroup lattice structure as for the lattice of subgroups of C_8 x C_2, although the groups are of course nonisomorphic.
		This is the Galois group of x^5 -2 over the rationals, and can be represented as the subgroup of S_5 generated by (2 3 5 4) and (1 2 3 4 5).
	www.math.usf.edu /~eclark/algctlg/small_groups.html (1543 words)

	group-examples - Microformats
		This page is to collect examples of groups and how members of groups / group memberships are organized and marked up.
		Note that the code below is _not_ from the main group but on a members page at http://www.flickr.com/groups_members.gne?id=41758902@N00.
		The following example is for a member of a group (http://www.youtube.com/group/mentosgeysercontestYouTube).
	microformats.org /wiki/group-examples (183 words)

	Examples of Groups
		Hope CLC, Taunton, MA Hope CLC, on one level, is a group of people who want to live life more fully and thus gather regularly.
		A few historical highlights include the discerned group apostolates of the early 1980's; "the people and situation of E1 Salvador," followed by "developmentally disabled adults of greater Taunton." We then felt called to an extensive year-long study of simple lifestyle issues around 1985-6.
		Going into the retreat, some in the group were feeling led to develop a common community mission, but not everyone felt ready for this.
	www.clc-usa.org /clc_examples.htm (867 words)

	Introduction to Groups (Site not responding. Last check: 2007-10-20)
		In this chapter, we shall consider in some detail the algebraic structure which will be of primary concern to us throughout, namely the notion of a group.
		Actually the reader has come in contact, during his or her mathematical career, with specific examples of groups as will be seen by the examples we shall give.
		All these examples have features in common which are desirable to axiomatize.
	web.usna.navy.mil /~wdj/tonybook/gpthry/node7.html (83 words)

	Supplementary ProofPower Examples
		The examples are supplied as PDF documents for you to read and as source tarballs so that you can experiment with them using ProofPower.
		This is followed by the definitions of the concepts of group, homomorphism between groups, subgroup, normal subgroup, kernel of a homomorphism, congruence modulo a subgroup, coset of a subgroup, and quotient group.
		Several examples of groups are exhibited and used to show that the various abstract notions lead to the expected theorems: e.g., that the exponential function is an isomorphism between the additive group of real numbers and the multiplicative group of positive real numbers.
	www.lemma-one.com /ProofPower/examples/examples.html (964 words)

	Science NetLinks: Groups We Belong To
		A very effective way to teach students about groups at this level is to use their own experiences to help them make explicit their intuitive notions about groups and related behavior.
		Once students have an understanding of groupings based on a single criterion, ease into the lesson by discussing things that will make them more aware of different kinds of groups and how one becomes a member—either through birth or by joining.
		Using books and magazines, show students pictures of people who are clearly members of different groups and ask them to identify the group, guess whether the person was born into or joined the group, describe what kinds of things members of the group do, and more.
	www.sciencenetlinks.com /lessons.cfm?BenchmarkID=7&DocID=341 (1010 words)

	Examples : Subsetting Groups of Data with the Having Condition
		The Having condition specifies the condition(s) that each group must satisfy in order to be included in the query output.
		You can use a Having condition to subset grouped data by using HAVING in the same query with a GROUPBY and a summary function.
		Which divisions in the previous example have a minimum education level that is greater than 15 years?
	www.asu.edu /it/fyi/unix/helpdocs/statistics/sas/sasdoc/sashtml/query/z1116676.htm (167 words)

	Addressing the Underlying Causes of Poverty -- University for a Night 2000 Recommendations
		This knowledge must both be protected legally and through economic policies that ensure that the indigenous people themselves benefit when such knowledge is shared and built upon.
		A key first step is educating indigenous people and other marginalized groups about their political and economic rights.
		Without realistic alternatives to narcotics trade, those involved in production (for example, cocaine in Andean countries) and sale in the more developed countries cannot be expected to leave this business.
	www.synergos.org /universityforanight/00/underlyingcauses.htm (744 words)

	An introduction to groups
		Another was that the composition of two moves, one after the other, was itself a move.
		These are, in fact, two of the conditions for the set of all legal moves of a permutation puzzle to form a group.
		Before giving the formal definition of a group in §5.3, we will first provide examples of groups that we have seen in earlier chapters.
	web.usna.navy.mil /~wdj/book/node163.html (179 words)

	Wallpaper Groups (Site not responding. Last check: 2007-10-20)
		You might like to look at the first section on transformations of the plane, then skip to the section on the 17 plane symmetry groups to get an idea of the different kinds of patterns.
		The sections on lattices, on transformation groups and symmetry, and on history are more technical and, perhaps, most appropriate for college-level readers.
		The concept of "group" is one of the most important concepts in mathematics, and a nice examples of groups are the wallpaper groups.
	www.clarku.edu /~djoyce/wallpaper (138 words)

	eChalk Online Classroom for K-12
		Some examples of groups that a district or school might create are the: Curriculum Development Department, Basketball Team, Spanish Club, PTA, etc.
		was designed specifically for K-12 schools and districts to accommodate the unique groups of people that want to communicate with each other within a school, between schools and with the wider community.
		Groups can be restricted so that only members can see what is within the group, opened up so that information about the group will be made public to the Internet and many combinations in between.
	www.echalk.com /r_groups.html (287 words)

Try your search on: Qwika (all wikis)