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	Glossary of group theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Group homomorphisms that have (The function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x) inverse functions.
		Every finite group is built up from simple groups through the use of (additional info and facts about group extensions) group extensions, so the study and classification of finite simple groups is central to the study of finite groups in general.
		Denoted by GL(n, F), is the group of n-by-n (additional info and facts about invertible matrices) invertible matrices, where the elements of the matrices are taken from a (A piece of land cleared of trees and usually enclosed) field F such as the real numbers or the complex numbers.
	www.absoluteastronomy.com /encyclopedia/g/gl/glossary_of_group_theory.htm (1286 words)

	[No title]
		Extensions to Local Network Modules other than Ethernet Other networks that directly support multicasting, such as rings or buses conforming to the IEEE 802.2 standard, may be handled the same Deering [Page 6] RFC 1112 Host Extensions for IP Multicasting August 1989 way as Ethernet for the purpose of sending multicast IP datagrams.
		Extensions to an Ethernet Local Network Module To support the reception of multicast IP datagrams, an Ethernet module must be able to receive packets addressed to the Ethernet multicast addresses that correspond to the host's IP host group addresses.
		Group Address Binding The binding of IP host group addresses to physical hosts may be considered a generalization of the binding of IP unicast addresses.
	www.rfc-editor.org /rfc/rfc1112.txt (4943 words)

	[No title]
		Extensions to Local Network Modules other than Ethernet Other networks that directly support multicasting, such as rings or buses conforming to the IEEE 802.2 standard, can be handled the same way as Ethernet for the purpose of sending multicast IP datagrams.
		Extensions to the IP Module To support the reception of multicast IP datagrams, the IP module must be extended to recognize the addresses of IP host groups to which the host currently belongs, in addition to the host's individual IP address(es).
		However, the fact that group addresses are location-independent (they are not statically bound to a single network interface) suggests possible uses as more general "logical addresses", both in the source as well as the destination address field of datagrams.
	www.mit.edu /afs/athena/reference/rfc/rfc988.txt (5328 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		There is a more general theory for topological group extensions whihc are bundles I think due to at least two people independently G.
		For G compact, > the central extensions correspond to the torsion part of H2(G), > which transgresses to all of H3(BG).
		In that case, there are > extensions of the Lie algebra which correspond to integral > cohomology classes in H2(G;Z), but which do not extend to group > extensions.) If we consider central extensions of the loop group > LG, then H2(LG) = H3(BLG), and every circle bundle corresponds to > a central extension.
	www.lehigh.edu /~dmd1/js820.txt (562 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.
		Groups acting on topological spaces are the basis of equivariant topology and homotopy theory in Algebraic Topology.
		Nielsen's theorem: subgroups of free groups are free.
	www.math.niu.edu /~rusin/known-math/index/20-XX.html (2774 words)

	RFC 1768 (rfc1768) - Host Group Extensions for CLNP Multicasting
		A multicast datagram is delivered to all members of its destination host group with the same "best-efforts" reliability as regular unicast CLNP datagrams, i.e., the datagram is not guaranteed to arrive intact at all members of the destination group or in the same order relative to other datagrams.
		In the development of multicast address extensions to CLNP, requirements were identified for: (1)"easily distinguishing" group addresses at the Network layer from NSAP addresses; (2)leaving the currently allocated address families unaffected and (3)ensuring that the approach taken would not require the establishment of new addressing authorities.
		Group Network addresses are defined by creating a new set of AFI values, one for each existing AFI value, and a fixed one-to-one mapping between each of the existing AFI values and a corresponding group AFI value.
	www.faqs.org /rfcs/rfc1768.html (11970 words)

	RFC 988 (Site not responding. Last check: 2007-10-08)
		RFC 988 July 1986 Host Extensions for IP Multicasting (X.25), all IP host group addresses might be mapped to the well-known local address of an IP multicast agent; an agent on such a network would take responsibility for completing multicast delivery within the network as well as among networks.
		RFC 988 July 1986 Host Extensions for IP Multicasting APPENDIX I. The Internet Group Management Protocol (IGMP) is used between IP hosts and their immediate neighbor multicast agents to support the creation of transient groups, the addition and deletion of members of a group, and the periodic confirmation of group membership.
		RFC 988 July 1986 Host Extensions for IP Multicasting the timers is intended to cause only the one member whose timer expires first to send a Confirm Group Request, stimulating a Reply to reset all the timers.
	www.ipv6tools.com /pages/rfc988.htm (5452 words)

	Extension Manager 4.0
		A package is a group of extensions that go together, either because they are from the same manufacturer or because the extensions rely on each other.
		Extensions Manager 4.0 uses the short version string to display the version of a file in its window, and it uses the long version string as the package identifier for each extension.
		Extensions Manager 4.0 incorporates tri-state checkboxes which let the user easily know that only some items in a group are on, just as the Installer lets you know that only some items in a custom install package will be installed, as in Figure 4.
	developer.apple.com /technotes/tn/tn1091.html (1347 words)

	IETF nntpext Working Group
		Also, a number of extensions to the protocol are now in common use (and yet more have been proposed), but most such extensions are only documented in the source code that implements them, or in associated release notes - not in the NNTP standard.
		Where there is widespread interest in a particular kind of extension, the internet user community would benefit from consensus among implementors prior to deployment, as to the particulars of that extension.
		The first concern of this working group shall be for the interoperability of the various NNTP implementations, and therefore for clear and explicit specification of the protocol.
	www.eyrie.org /~eagle/nntp/ietf.html (698 words)

	The COFI-Language Group Home Page
		CASL-LTL is an extension to overcome this limit, allowing to specify dynamic system by modelling them by means of labelled transition systems and by expressing their properties with temporal formulae.
		It is based on LTL a logic-algebraic formalism for the specification of concurrent systems mainly devoleped by E.Astesiano and G. Reggio (see more papers section).
		A corresponding adaptation of the CASL Summary, as well as a document describing the semantics in more detail, is in preparation, and is to be made available at a later date.
	www.informatik.uni-bremen.de /cofi/Language/PROJECTS/extensions.html (784 words)

	Project Groups (Site not responding. Last check: 2007-10-08)
		The user can edit any Group and modify the directory to be searched and the filename extensions to be included.
		Groups can also be used to filter the files which are viewed in the Classpath or the Folders area.
		If a group is chosen from the drop-down menu on the menubar, only files with the appropriate extensions will be viewed.
	www.datarepresentations.com /support/docs/sfj/standard/ide6.htm (177 words)

	W3C Rule Interchange Format (RIF) WG Proposed Charter
		This Working Group is chartered to produce a core rule language plus extensions which together allow rules to be translated between rule languages and thus transferred between rule systems.
		The Working Group is chartered to first establish the extensible core and possibly a set of extensions, and then (in Phase 2) to begin to specify additional extensions based on user requirements.
		The XML Schema Working Group provides a way to define XML grammars, which may be useful in defining the rule format syntax, and a model for data types and data structures.
	www.w3.org /2005/07/rules/charter2 (4384 words)

	Third-party Tools and Extensions for Group Policy
		Group Policy allows administrators to efficiently implement security settings, enforce IT policies, and distribute software consistently across a given site, domain, or range of organizational units.
		Through Group Policy, you can enforce consistent security and configuration policies across these heterogeneous systems using the same familiar tools and processes you use to manage your Windows systems.
		DirectControl provides a wide range of group policies designed specifically for individual platforms that enable you to apply consistent updates to the sudoers file and maintain consistent automount settings for groups of users or systems.
	www.microsoft.com /windowsserver2003/technologies/management/grouppolicy/gptools.mspx (1136 words)

	Welcome to Shell+ Home
		An icon handler is a type of Shell extension that allows you to dynamically assign icons to the members of a file class.
		A copy hook handler is a Shell extension that determines if a Shell folder or printer object can be moved, copied, renamed, or deleted.
		A few steps only are necessary to implement this type of Shell extension.
	www.shellplus.com /shell-extensions-map.html (1280 words)

	John Greschak - Finale Suggestion 295: Default Tuplet Extensions for Various Configurations
		IWBNI it were possible to specify default left and right tuplet extensions as a function of the type of object (e.g.
		The size of the possible extensions that might be used for a given type of note or rest could be specified by four numbers.
		Finally, when a bracket is placed on the note side of a beamed group, the extensions specified for non-beamed notes could be used.
	www.greschak.com /notation/finale/iwbni/fs295.htm (530 words)

	TOPOLOGICAL METHODS IN GROUP THEORY
		First, it is for graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric and homological group theory.
		Secondly, I am writing for group theorists who would like to know more about the topological side of their subject but who have been too long away from topology.
		5.13 Semistability of group extensions and ascending HNN extensions
	www.math.binghamton.edu /ross/contents.html (289 words)

	ipedia.com: Saunders Mac Lane Article (Site not responding. Last check: 2007-10-08)
		He started writing on group extensions in 1942, and collaborated with Samuel Eilenberg from 1943, on what are now called Eilenberg-MacLane spaces K(π,n), having a single non-trivial homotopy group (π, in dimension n).
		This work opened the way to group cohomology in general.
		After the introduction via the Eilenberg-Steenrod axioms of the abstract approach to homology theory, he became one of the developers of category theory.
	www.ipedia.com /saunders_mac_lane.html (308 words)

	Fast Fourier Analysis for Abelian Group Extensions - Rockmore (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: Let G be a finite group and f any complex-valued function defined on G and ae an irreducible complex matrix representation of G. The Fourier transform of f at ae is defined to be the matrix P s2G f(s)ae(s).
		The Fourier transforms of f at all the irreducible representations of G determine f via the Fourier inversion formula f(s) = 1 jGj P ae d ae trace(b f(ae)ae(s \Gamma1)): Direct computation of all Fourier transforms of f involves on the order of j G j 2 operations as does direct...
		The first results of this type obtained for nonabelian groups are due to Willsky.
	citeseer.ist.psu.edu /149256.html (615 words)

	Category Theory
		Any monoid (and thus any group) can be seen as a category: in this case, the category has only one object and the morphisms of the category are given by the elements of the monoid.
		Indeed, from a categorical point of view, a set-theoretical cartesian product, a direct product of groups, a direct product of abelian groups, a product of topological spaces and a conjunction of propositions in a deductive system are all instances of a categorical concept: the categorical product.
		We said "almost", because when one looks at their 1942 paper "Group Extensions and Homology", one discovers specific functors and natural transformations at work, limited to groups.
	plato.stanford.edu /entries/category-theory (7029 words)

	Shift Endomorphisms And Compact Lie Extensions - Coelho, Parry (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: We consider skew-products with an arbitrary compact Lie group, when the base map is a one-sided shift of finite type endowed with an equilibrium state of a Holder continuous function.
		We show that for a generic set of equilibrium states the isomorphism class of the skew-products corresponds essentially to...
		Two sided such extensions are Bernoulli [Ru] and isomorphic to their bases.
	citeseer.ist.psu.edu /coelho95shift.html (377 words)

	Chistory
		For example, functions with pointer arguments derived from arrays are hard to compile into efficient code on vector machines, because it is seldom possible to determine that one argument pointer does not overlap data also referred to by another argument, or accessible externally.
		Finally, despite the changes that it has undergone since its first published description, which was admittedly informal and incomplete, the actual C language as seen by millions of users using many different compilers has remained remarkably stable and unified compared to those of similarly widespread currency, for example Pascal and Fortran.
		Perhaps the most significant extensions are the `far' and `near' pointer qualifications intended to deal with peculiarities of some Intel processors.
	cm.bell-labs.com /cm/cs/who/dmr/chist.html (8388 words)

	Publications
		Melbourne, M. Nicol and A. Török [2005] Statistical properties of compact group extensions of hyperbolic flows and their time one maps.
		Melbourne and A. Török [2003] Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions.
		Nicol [2003] Stable transitivity of Euclidean group extensions.
	www.maths.surrey.ac.uk /research/General/publications.html (6339 words)

	Linnell, P and Schick, T.: Finite group extensions and the Atiyah conjecture (Site not responding. Last check: 2007-10-08)
		We prove that these conditions are fulfilled for a certain class of groups, which contains in particular Artin's pure braid groups (and more generally fundamental groups of fiber-type arrangements), free groups, fundamental groups of orientable compact surfaces, certain knot and link groups, primitive positive one-relator groups, and products of these.
		In the course of the proof we prove that if these extensions are torsion-free, then they have plenty of non-trivial torsion-free quotients which are virtually nilpotent.
		Finite group extensions and the Baum-Connes conjecture (also on the arXiv), where the Baum-Connes conjecture is proved e.g.
	www.uni-math.gwdg.de /schick/publ/extAtiyah.html (226 words)

	DNS Extensions (dnsext) Charter
		DNS Security Extension Clarification on Zone Status (RFC 3090) (0 bytes)
		Applicability Statement for DNS MIB Extensions (RFC 3197) (0 bytes)
		DNS Extensions to support IP version 6 (RFC 3596) (0 bytes)
	www.ietf.org /html.charters/dnsext-charter.html (998 words)

	Point-to-Point Protocol Extensions (pppext) Charter
		The Point-to-Point Protocol (PPP, RFC 1661) is a mature protocol with a
		Class Extensions for PPP over ATM Adaptation Layer 2 (13620 bytes)
		Point-to-Point Protocol Extensions for Bridging (RFC 1220) (0 bytes)
	www.ietf.org /html.charters/pppext-charter.html (718 words)

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