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	Simple group - Wikipedia, the free encyclopedia
		In mathematics, a simple group is a group which is not the trivial group and whose only normal subgroups are the trivial group and the group itself.
		The finite simple groups are important because in a certain sense they are the "basic building blocks" of all finite groups, somewhat similar to the way prime numbers are the basic building blocks of the integers.
		Simple groups of infinite order also exist: simple Lie groups and the infinite Thompson groups T and V are examples of these.
	en.wikipedia.org /wiki/Simple_group (208 words)

	Simple Lie group - Wikipedia, the free encyclopedia
		These groups, and groups closely related to them, include many of the so-called classical groups of geometry, which lie behind projective geometry and other geometries derived from it by the Erlangen programme of Felix Klein.
		The complete list of simple Lie groups is the basis for the theory of the semisimple Lie groups and reductive groups, and their representation theory.
		Such groups are classified using the prior classification of the complex simple Lie algebras: for which see the page on root systems.
	en.wikipedia.org /wiki/Simple_Lie_group (498 words)

	Simple article - Simple interval octave compound mathematics algebra simple ideals simple - What-Means.com (Site not responding. Last check: 2007-10-21)
		In music a simple interval which lies within one octave, contrasted with a compound interval which exceeds or is wider than one octave.
		A group is a simple group if it has no non-trivial normal subgroup.
		The Simple shoes (http://www.simpleshoes.com) brand is popular among surfing and skateboarding enthusiasts.
	www.what-means.com /encyclopedia/Simple (114 words)

	Classification of finite simple groups - Iridis Encyclopedia (Site not responding. Last check: 2007-10-21)
		The classification of the finite simple groups is a vast body of work in mathematics, mostly published between around 1955 and 1983, which classifies all of the finite simple groups.
		Five of the sporadic groups were discovered by Mathieu in the 1860s and the other 21 were found between 1965 and 1975.
		In particular, during the original proof, nobody knew how many sporadic groups there would be, and in fact some of the sporadic groups (for example, the Janko groups) were discovered in the process of trying to prove the classification theorem.
	www.iridis.com /tzsb/Classification_of_finite_simple_groups (424 words)

	PlanetMath: characteristically simple group
		Any finite characteristically simple group is the direct product of several copies of
		Cross-references: simple groups, isomorphic, direct product, finite, characteristic subgroups, group
		This is version 4 of characteristically simple group, born on 2002-12-16, modified 2004-05-12.
	planetmath.org /encyclopedia/CharacteristicallySimpleGroup.html (65 words)

	PlanetMath: simple group
		See Also: group, subgroup, group homomorphism, quotient group, Feit-Thompson theorem
		This is version 3 of simple group, born on 2002-02-19, modified 2002-02-20.
		(Group theory and generalizations :: Structure and classification of infinite or finite groups :: Simple groups)
	planetmath.org /encyclopedia/Simple.html (68 words)

	Introduction
		Because many of a groups properties can be determined by the nature of its composition series, the study of simple groups has great importance for the study of groups in general.
		Between 1966 and 1975, 19 more sporadic simple groups were discovered, but it was thought that the problem would not be solved until the year 2000.
		Theorem: There is a list consisting of 18 infinite familes of simple groups and 26 sporadic simple groups not belonging to these families such that every finite simple group is isomorphic to one of the groups in the list.
	www-math.cudenver.edu /~rrosterm/simple/node1.html (425 words)

	Reading Group Guide \| SIMPLE ABUNDANCE by Sarah Ban Breathnach (Site not responding. Last check: 2007-10-21)
		Simple Abundance shows you how your daily life can be an expression of your authentic self...as you chose the tastiest vegetables from your garden, search for treasures at flea markets, establish a sacred space in your home for meditation, and follow the rhythmn of the seasons and the year.
		To get started, think of examples, such as a Shaker chair, which is at once austerely simple, but luscious and even extravagant in its perfect shape.
		GRATITUDE JOURNAL (see January 14 in Simple Abundance)--For one week preceding the reading group meeting, each evening jot down five things that you were grateful for that day.
	www.readinggroupguides.com /guides/simple_abundance.asp (1043 words)

	No Title (Site not responding. Last check: 2007-10-21)
		Finite simple groups and finite primitive permutation groups,Bull.
		Symmetric graphs and the classification of the finite simple groups, in Groups Korea 1983, Lecture Notes in Mathematics 1098, Springer, Berlin, Heidelberg, New York, 99-110.
		On primitive representations of finite alternating and symmetric groups with a 2-transitive subconstituent, (with Jie Wang), J.
	www.maths.uwa.edu.au /~praeger/CV/cherylpubs (5292 words)

	Group Theory & Rubik's Cube
		Group theory is the study of the algebra of transformations and symmetry.
		Given an element x of a group G, the orbit of x is the set of all elements of G which are generated by x, i.e.
		A representation of a group G is a set of matrices M which are homomorphic to the group.
	akbar.marlboro.edu /~mahoney/courses/Spr00/rubik.html (3602 words)

	A Simple Machines Activity (Site not responding. Last check: 2007-10-21)
		Each group will be required to find a minimum of six examples of their assigned simple machine and one example of a pulley for the interactive bulletin board.
		Each group will make a key for their simple machine, fold it, and place it in the back of the sentence strip pocket.
		In that case the student or group would be responsible for finding all the examples for their project and gluing them in a file folder.
	www.richlandclicks.org /Teacher/connections/grade3/simplemachine.htm (858 words)

	The Java Community Process(SM) Program - JSRs: Java Specification Requests - detail JSR# 165
		SIMPLE is an extension of SIP to support presence and instant messaging.
		SIMPLE is an IETF working group that advanced a set of extensions to SIP to support presence and instant messaging.
		SIMPLE is a set of extensions made to the SIP protocol to support presence and instant messaging.
	www.jcp.org /en/jsr/detail?id=165 (1150 words)

	Messaging vendors rally around SIMPLE protocol
		SIMPLE is based on the Session Initiation Protocol, a signaling protocol used to establish Internet telephone calls, multimedia conferences, chat sessions and interactive communications.
		SIMPLE is one of three approaches to instant messaging proposed to the IETF, which has been struggling to reach consensus in this area for several years.
		The SIMPLE working group will meet this week in London to debate a few remaining technical issues, including how to set up communications for large messages and multimedia, and how users will authorize the release of their presence information to other subscribers.
	www.networkworld.com /archive/2001/123534_08-06-2001.html (895 words)

	Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups
		This function returns the index into the sequence of class representatives of the group designated by name (either a string or a simple group record) of the class with name classname.
		Given a process P which currently points to a group, return the string describing the maximal subgroups of the group.
		Given a process P which currently points to a group, modify it so that it points to the next group if there is one or make it empty if there is not.
	www.math.uiuc.edu /Software/magma/text77.html (579 words)

	simple algebra (Site not responding. Last check: 2007-10-21)
		Simple Algebra -- from MathWorld Simple Algebra -- from MathWorld An algebra with no nontrivial ideals.
		See also: simple group This article is a stub...
		A central simple algebra A (over K) is an algebra A over K, which is finite dimensional as a vector space over K, such that...
	learning-gd.com /articles/290/simple-algebra.html (218 words)

	Simple groups (Site not responding. Last check: 2007-10-21)
		For an arbitrary group, G, we recall that G and e are normal subgroups, if these are the only ones we say the group is simple.
		In other words, this is the program to discover all finite simple groups and to prove that there are no more to be found.
		There are other families of finite simple groups, but their determination is beyond the scope of this book.
	web.usna.navy.mil /~wdj/tonybook/gpthry/node34.html (580 words)

	Group Key Management
		A simple group key management protocol was implemented as part of the development of secure PVM (tech report, 240KB).
		Besides matching the hierarchical nature of the military command structure, this approach is primarily of interest because it permits the rapid distribution of session keys for a large number of users in a manner that efficiently uses the bandwidth-limited wireless medium.
		We first sketch some multicast group parameters that are relevant to security, and outline the basic security issues concerning multicast in general, with emphasis on IP multicast.
	www.csm.ornl.gov /~dunigan/gkm.html (1480 words)

	Reading Group Guide: Simple Abundance by Sarah Ban Breathnach (Site not responding. Last check: 2007-10-21)
		When she first started writing, Sarah Ban Breathnach thought she was writing a book about downshifting, but as she worked on paring down by shedding the unnecessary from her life, she found that she was having to make choices.
		In order to make these choices she had to decide what was important to her, and with each decision she was learning more and more about who she really was.
		In Simple Abundance you will discover the person you really are, buried under all the excess--excess obligations, excess belongings, excess clutter.
	www.twbookmark.com /books/42/0446519138/reading_guide8910.html (1136 words)

	Database of Almost-Simple Groups
		The groups G and S are as above the almost simple group G and its socle, the simple group S. Let A be the full automorphism group of S, and let F< x, y > be a free group on two generators, called x and y..
		Use the information in the database to construct a monomorphism f from the almost simple group G into A, the permutation representation of the full automorphism group of its socle stored in the database.
		The algorithms used to deal with the alternating and symmetric groups not in the database are by Derek Holt, starting from the paper of Bratus and Pak [BP00].
	www.math.niu.edu /help/math/magmahelp/text454.html (935 words)

	Diamond Theory: Symmetry in Binary Spaces (Site not responding. Last check: 2007-10-21)
		For example, the affine group A on the 4-space over the 2-element field has a natural noncontinuous and asymmetric but symmetry-preserving action on the elements of a 4x4 array.
		In the 4x4 case, D is a four-diamond figure (left, below) and G is a group of 322,560 permutations generated by arbitrarily mixing random permutations of rows and of columns with random permutations of the four 2x2 quadrants.
		A table of the octahedral group O using the 24 patterns from the 2x2 case of the diamond theorem.
	m759.freeservers.com /index.html (1917 words)

	Cover Pages: IETF SIMPLE Specifications Support Presence-Based IM, Video, and Voice.
		SIMPLE, which stands for SIP for Instant Messaging and Presence Leveraging Extensions, is a clearly contrived acronym that describes a body of work going on in the Internet Engineering Task Force (IETF).
		The IETF SIMPLE group is defining numerous extensions to PIDF to convey rich presence data.
		These policy systems can be extremely simple, allowing a user to accept or block requests based solely on the identity of the requestor, to extremely complex, allowing for time based rules that grant or deny specific pieces of information.
	xml.coverpages.org /ni2004-02-17-a.html (13378 words)

	SDSI - A Simple Distributed Security Infrastructure
		Also, there is no public-key for a group, so that the second method has the slight disadvantage that the principal playing that role signs with his full authority, rather than with the authority restricted to the permissions of his role.
		That is, it is is a simplified definition of the group that is equivalent to the original definition, given what the server already knew and what credentials it had to work with.
		For example, it may be just an edited or simplified top-level definition of the group, with all individual principals deleted, non-failing group names or sub-forms removed, and thresholds decreased by the number of successful top-level forms contained in the original threshold form before editing.
	theory.lcs.mit.edu /~rivest/sdsi10.html (11912 words)

	A presentation for the Thompson sporadic simple group - Havas, Soicher, Wilson (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		0.5: Geometries for the group PSL(3; 4) - Harald Gottschalk Mlu (1999)
		A presentation for the Thompson sporadic simple group.
		1 Geometry of Sporadic Groups I: Petersen and Tilde Geometries (context) - Ivanov - 1999
	citeseer.ist.psu.edu /havas01presentation.html (517 words)

	The Java Community Process(SM) Program - JSRs: Java Specification Requests - detail JSR# 164
		SIMPLE Presence provides a standard portable and secure interface to manipulate presence information between a SIMPLE client (watcher) and a presence server (presence agent).
		SIMPLE Presence API is intended to be a standard API to presence in the SIMPLE protocol (i.e., SIP augmented with presence capabilities).
		SIMPLE is a set of natural extensions made to the SIP protocol to support presence and instant messaging.
	jcp.org /en/jsr/detail?id=164 (1234 words)

	FITSDIN - Reads a FITS disc file composed of simple, group or table objects
		There is an option to run in automatic mode, where the names of output NDF data structures are generated automatically, and you can decide whether or not format conversion is to be applied to all files (rather than being prompted for each).
		For group-format data the group parameters are evaluated and appended to the full header.
		The group parameters are evaluated using their scales and offsets, and made to look like FITS cards, whose keywords are derived from the values of PTYPEm in the main header.
	star-www.rl.ac.uk /star/dvi/sun95.htx/node258.html (1652 words)

	SIP for Instant Messaging and Presence Leveraging Extensions (simple) Charter
		The working group will work within the framework for presence and IM described in RFC 2778.
		SIP working group, and then use them here.
		Submission of SIMPLE PIDF profile to IESG for publication as Proposed Standard
	www.ietf.org /html.charters/simple-charter.html (953 words)

	On The Graph Of Generating Sets Of A Simple Group - Pak (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		This is related to the recent conjecture of Diaconis and Graham.
		Introduction Let G be a finite group, and let --(G) be the minimal number of generators of G.
		Pak, On the graph of generating sets of a simple group, preprint (1999).
	citeseer.ist.psu.edu /pak99graph.html (641 words)

	Spirituality & Religion: Keep_It_Simple_Sister Group on Care2 Connect (Site not responding. Last check: 2007-10-21)
		This is a closed group and is accessible to members only.
		Keep It Simple Sister: is a group for women only over the age of 21 who seek to share ideas and to help each other out not only spiritually but with everyday living.
		Even though the group is set up for Pagans/Heathans, there is plenty of information withi
	www.care2.com /c2c/group/KISS (93 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Let G be a group of order 160 = 5*2^5, and let P be a Sylow 2-subgroup of G. Then P has index 160/32 = 5 in G. Let S be the set of cosets gP of P in G and let G act on S by left multiplication.
		Thus there is a homomorphism from G into S_5, the permuation group on 5 letters.
		But there can't be a simple group of order 40 since a group of such order must have 1 Sylow-5 group (a normal subgroup) (Any group which is simple and has order 52^j must have j>=4 so it can have more than 1 Sylow-5 group*).
	www.math.niu.edu /~rusin/known-math/00_incoming/160gp (538 words)

	► » Simple group(s) of order 504? (Site not responding. Last check: 2007-10-21)
		group is transitive (which itself follows from the more general result
		stabilizer is a nontrivial normal subgroup of a 2-transitive group of
		that a nontriival normal subgroup of a primitive group is transitive).
	www.science-chat.org /Simple-groups-of-order-504-6924179.html (1540 words)

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