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	Janko group - Wikipedia, the free encyclopedia
		Janko found a modular representation in terms of 7 × 7 matrices in the field of eleven elements, with generators given by
		It is a subgroup of index two of the group of automorphisms of the Hall-Janko graph, leading to a permutation representation of degree 100.
		The fourth Janko group was shown to be probable by Janko in 1976, and then proven to uniquely exist by Simon Norton in 1980.
	en.wikipedia.org /wiki/Janko_group (507 words)

	Janko group -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, the Janko groups J
		The third Janko group, also known as the Higman-Janko-McKay group, is a finite simple sporadic group of order 50232960.
		Richard Weiss, "A Geometric Construction of Janko's Group J
	www.absoluteastronomy.com /encyclopedia/j/ja/janko_group.htm (499 words)

	Encyclopedia: Chevalley group (Site not responding. Last check: 2007-10-22)
		In mathematics, a cyclic group is a group that can be generated by a single element, in the sense that the group has an element a (called a generator of the group) such that every element of the group is a power of a.
		In mathematics, the general linear group of degree n over a field F (such as R or C), written as GL(n, F), is the group of n×n invertible matrices with entries from F, with the group operation that of ordinary matrix multiplication.
		In group theory, the Schur multiplier is the second homology group of a group G with coefficients in the integers,.
	www.nationmaster.com /encyclopedia/Chevalley-group (2128 words)

	Conway group - Wikipedia, the free encyclopedia
		In mathematics, the Conway groups Co, Co, and Co are three sporadic groups discovered by John Horton Conway.
		is obtained by dividing the automorphism group of Λ by its center, which consists of the scalar matrices ±1.
		The groups Co (of order 42,305,421,312,000) and Co (of order 495,766,656,000) consist of the automorphisms of Λ fixing a lattice vector of length 2 and a vector of √6 respectively.
	en.wikipedia.org /wiki/Conway_group (254 words)

	Department of Mathematics - Richard Weiss (Site not responding. Last check: 2007-10-22)
		A Characterization of the Group $Co_3$ as a Transitive Extension of $HS$
		A Geometric Characterization of the Groups $McL$ and $Co_3$
		A Characterization of the Groups $Fi_{22}$, $Fi_{23}$ and $Fi_{24}$ (Co-author: J. van Bon)
	www.tufts.edu /as/math/weiss.html (156 words)

	Janko group - Wikipedia, the free encyclopedia
		are four of the twenty-six sporadic groups; their respective orders are:
		The group is also called the Hall-Janko group or the Hall-Janko-Wales group, since it was predicted by Janko and constructed by Hall and Wales.
		Evidence for its existence was uncovered by Janko, and it was shown to exist by Higman and McKay.
	www.wikipedia.org /wiki/Janko_group (507 words)

	School of Mathematics
		According to the classification of the finite simple groups, announced in the 1980's, the simple groups fall into finitely many classes of groups having similar structure to each other, together with one class of 26 so-called sporadic simple groups.
		Among the groups acting on such geometries are a large number of sporadic groups, including both the Monster and the baby Monster sporadic simple groups.
		He is working towards a permutation-theoretic characterization of automorphism groups of recursively saturated structures; this could allow one to recover some structure of models from their automorphism groups.
	www.mat.bham.ac.uk /research/pure/research.htm (2055 words)

	Knowledge King - Conway group (Site not responding. Last check: 2007-10-22)
		Conway, J. A perfect group of order 8,315,553,613,086,720,000 and the sporadic simple groups.
		The largest, Co (of order 8,315,553,613,086,720,000), is obtained by dividing the automorphism group of Λ by its center, which consists of the scalar matrices ±1.
		The groups Co and Co both contain the McLaughlin group McL (of order 898,128,000) and the Higman-Sims group (of order 44,352,000), which can be described as the pointwise stabilizers of a 2-2-√6 triangle and a 2-√6-√6 triangle respectively.
	www.knowledgeking.net /encyclopedia/c/co/conway_group.html (255 words)

	[No title]
		Finite simple groups and localization Jose L. Rodriguez, Jer^ome Scherer and Jacques Thevenaz * Abstract The purpose of this paper is to explore the concept of localization, wh* ich comes from homotopy theory, in the context of finite simple groups*.
		In some ca* ses, we also consider automorphism groups* and universal covering groups and we sho* w that a localization of a finite simple group* may not be simple.
		The Conway groups are com* plete, the smaller ones are maximal simple subgroups of Co1 and there is a unique conj *ugacy class of each of them in Co1 as indicated in the ATLAS [4, p.180].
	hopf.math.purdue.edu /Rodriguez-Scherer-Thevenaz/simplegroups.txt (6910 words)

	Publications
		The residually weakly primitive geometries of the Dihedral Groups.
		with C.Lefèvre-Percsy and N.Percsy, New geometries for finite groups and polytopes.
		with H.Gottschalk, The Residually Weakly Primitive Geometries of the Janko Group J(1).
	cso.ulb.ac.be /~dleemans/papersbyyear.html (536 words)

	Higman (Site not responding. Last check: 2007-10-22)
		Despite the large amount of activity in group theory which was going on in Manchester, Higman was ambitious and began to apply for professorships.
		He published on units in group rings, the subject of his doctoral thesis, in 1940 then there was a break in his publication record during the time he worked in the Meteorological Office.
		His paper Embedding theorems for groups written jointly with both Bernhard Neumann, who as we noted was a colleague of Graham Higman's at Manchester at that time, and with Hanna Neumann, introduces the now standard group construction of HNN extensions (Higman - Neumann - Neumann extensions).
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Higman.html (1320 words)

	[ref] 71 The Character Table Library
		Note that the Brauer table and the corresponding ordinary table of a group determine the decomposition matrix of the group (or the decomposition matrices of its blocks).
		Generic character tables provide a means for writing down the character tables of all groups in a (usually infinite) series of similar groups, e.g., cyclic groups, or symmetric groups, or the general linear groups
		While the numbers of conjugacy classes for the members of a series of groups are usually not bounded, there is always a fixed finite number of types (equivalence classes) of conjugacy classes; very often the equivalence relation is isomorphism of the centralizers of the representatives.
	www.math.niu.edu /help/math/gap4/ref/CHAP071.htm (5881 words)

	GAP Manual: 48.12. CharTable
		The columns of the table will be sorted in the same order, as the classes of the group, thus allowing a bijection between group and table.
		The computation of character tables needs to identify the classes of group elements very often, so it can be helpful to store a class list of all group elements.
		for the Sylow 2 subgroup of the alternating group A_(11).
	www.math.uiuc.edu /Software/GAP-Manual/CharTable.html (881 words)

	Standard generators for J_3 (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Abstract: this paper we develop these ideas further, in the context of the simple group J 3.
		This group was chosen firstly because it has an outer automorphism group of order 2, which introduces extra complications, and secondly because it is reasonably small (of order 50232960) so we can do quite a large number of calculations in the group.
		Group Actions on Arrangements of Linear Subspaces and..
	citeseer.ist.psu.edu /553491.html (381 words)

	Subgroups of Finite Index
		Once a new definition has been made, the group relations are traced in an attempt to deduce further entries or to infer that this partial table will not extend to a table corresponding to a new class of subgroups.
		There is some evidence to suggest that better performance is achieved in those groups having one or more very long relators by deferring application of these relators until such time as a complete coset table has been obtained.
		The constructions of the previous section together with the Boolean function IsMaximal may be used to locate large maximal subgroups in a finite group.
	www.math.niu.edu /help/math/magmahelp/text301.html (3419 words)

	Nanotechnology combined with superconductivity could pave the way for "spintronics".
		At the base is a layer of diluted magnetic semiconductor, a type of material Janko and his group have been studying intensively.
		For example, an electric current flowing through the superconductor will cause a given flux tube to move to one side (with the patch of spins underneath moving along with it), while a current flowing in the reverse direction will move it back to the other side (see animation at right).
		Although Janko and his colleagues have tested their approach so far only through computer simulations, experiments are now underway to demonstrate the technique in the laboratory.
	www.talkaboutalternative.com /group/alt.ufo.reports/messages/96438.html (546 words)

	[No title]
		Theorem A. For any finite group G, there is an essential fixed point free 2-d* imensional (finite) Z-acyclic G-complex if and only if G is isomorphic to one of the simpl e groups* P SL2(2k) for k 2, P SL2(q) for q 3 (mod 8) and q 5, or Sz(2k) for odd k 3.
		Note in particular that B (~=Fqo Cq-1or ~=Fqo C(q-1)=2) is represented by the* * group of upper triangular matrices, and that D2(q-1)is the subgroup of monomial matrices* *.
		We choose M3 to be the group of monomial matrices with respect to the orthonormal basis {e1; e2; e3}.
	hopf.math.purdue.edu /Oliver-Segev/2dim.txt (17766 words)

	Construction of maximal subgroups in a large finite group (Site not responding. Last check: 2007-10-22)
		Construction of maximal subgroups in a large finite group
		Constructions for computing with subgroups defined by coset tables may be used to locate large maximal subgroups in a finite group.
		Thus after 30 tries we have constructed maximal subgroups of index 100, 315 and 1008.
	magma.maths.usyd.edu.au /magma/Examples/node16.html (114 words)

	LMS Proceedings Abstract, paper PLMS 1379 (Site not responding. Last check: 2007-10-22)
		Broué's abelian defect conjecture suggests a deep link between the module categories of a block of a group algebra and its Brauer correspondent, viz.
		We are able to verify Broué's conjecture for the Hall--Janko group, even its double cover $2.J_2$, as well as for $U_3(4)$ and ${\rm Sp}_4(4)$.
		In fact we verify Rickard's refinement to Broué's conjecture and show that the derived equivalence can be chosen to be a splendid equivalence for these examples.
	www.lms.ac.uk /publications/proceedings/abstracts/p1379a.html (84 words)

	Codes, Designs and Graphs from the Janko (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Groups J 1 and J 2 J. Key Department of Mathematical Sciences Clemson...
		Abstract: We construct some codes, designs and graphs that have the first or second Janko group, J1 or J2, respectively, acting as an automorphism group.
		We show computationally that the full automorphism group of the design or graph in each case is J1, J2 or J2, the extension of J2 by its outer automorphism, and we show that for some of the codes the same is true.
	citeseer.ist.psu.edu /629095.html (354 words)

	Cases for which the conjecture has been verified (Site not responding. Last check: 2007-10-22)
		The principal block of the Janko group J
		The non-principal block of the O'Nan group O'N with defect group C
		The non-principal block of the Higman-Sims group HS with defect group C
	www.stats.bris.ac.uk /~majcr/adgc/which.html (636 words)

	GAP Manual: 23 Finitely Presented Groups
		A finitely presented group is a group generated by a set of abstract generators subject to a set of relations that these generators satisfy.
		Note that the generators of the free group are different from the generators of the finitely presented group (even though they print with the same name).
		Finitely presented groups are after all groups, thus in principle all group functions are applicable to them (see chapter Groups).
	parallel.rz.uni-mannheim.de /gap/htm/CHAP023.htm (9357 words)

	Oxford University Press (Site not responding. Last check: 2007-10-22)
		This text illustrates how different methods of finite group theory including representation theory, cohomology theory, combinatorial group theory and local analysis are combined to construct one of the last of the sporadic finite simple groups - the fourth Janko group J 4.
		Aimed at graduates and researchers in group theory, geometry and algebra, Ivanov's approach is based on analysis of group amalgams and the geometry of the complexes of these amalgams with emphasis on the underlying theory.
		Readership: Graduate students and researchers in pure mathematics, particularly in group theory, geometry and algebra.
	www5.oup.com /isbn/0-19-852759-4 (203 words)

	[No title]
		The cohomology in degree $1$ of the group $F\sb 4$ in characteristic $2$ with coefficients in a simple module.
		On the $1$-cohomology of the groups $G\sb 2(2\sp n)$.
		The Green ring and modular representations of finite groups of Lie type.
	www.math.ufl.edu /fac/facmr/Sin.html (294 words)

	Resume
		``Simple groups with a standard 3-component of type Sp(6,2)'', Institute for Advanced Study, Princeton, NJ, March 1979.
		``Finite groups with a standard component isomorphic to a sporadic simple group'', NSF Conference on Finite Simple Groups, Duluth, MN, August, 1976.
		``Maximal subgroups of the Higman Janko McKay Group'', presented by coauthor A. Rudvalis, University of Chicago, Chicago, IL, June, 1972.
	www.ccs.neu.edu /home/laf/Resume.htm (1803 words)

	Hall-Janko graph - Wikipedia, the free encyclopedia
		It was constructed by Hall and D. Wales, and should probably therefore be called the Hall-Wales graph.
		Its group of automorphisms has a subgroup of index two which is the second Janko group, also known as the Hall-Janko group.
		This page was last modified 15:15, 8 January 2005.
	www.wikipedia.org /wiki/Hall-Janko_graph (105 words)

	Janko Laya Mountain Group - Climbing - Outback Bolivia
		Janko Laya Mountain Group - Climbing - Outback Bolivia
		Climb this seldom visited mountains located next to the beautifull Hichukhota valley.
		The Janko Laya at 5545 mts (18192 ft), the Chachacomani at 6074 mts (19,928 ft) or the Jalli Huaykunka at 5392 mts (17,690 ft) are some of this isolated and beautiful mountains.
	www.outbackbolivia.com /janko-laya_fr.html (53 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		1973 Maximal subgroups of the Hall-Janko-Wales group, Journal of Algebra, 24, 486-493, (with L. Finkelstein).
		41-54 in Finite Groups '72, Proceedings of the Gainesville Group Theory Conference edited by T. Gagen, M. Hale, and E. Shult, North Holland/American Elsevier, New York, (with J. Frame).
		1974 Maximal subgroups of the Higman-Janko-McKay group, Journal of Algebra, 30, 122-143, (with L. Finkelstein).
	www.math.umass.edu /Fac_Staff_Students/Faculty/Rudvalis/publ (144 words)

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