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Topic: PSL(2,7)

	PSL(2,7) (Site not responding. Last check: 2007-10-18)
		The projective special linear group G = PSL(2,7) is a finite group in mathematics that has important applications in algebra, geometry, and number theory.
		Then G = PSL(2,7) is defined to be the quotient group SL(2,7) / {I,−I} obtained by identifying I and −I. In this article, we let G denote any group isomorphic to PSL(2,7).
		However, PSL(2,7) is also isomorphic to SL(3,2) (= GL(3,2)), the special (general) linear group of 3×3 matrices over the field with 2 elements.
	publicliterature.org /en/wikipedia/p/ps/psl_2_7_.html (475 words)

	Octonion Products (Site not responding. Last check: 2007-10-18)
		PSL(2,7) is the 168-element simple group that is the central quotient group of SL(2,7).
		SL(2,7) is the 336-element group of 2x2 matrices with determinant 1 whose entries are elements of the finite group Z7.
		If Z7 is represented by the vertices of a heptagon, then PSL(2,7) is the linear fractional group of the vertices of the heptagon.
	www.valdostamuseum.org /hamsmith/480op.html (3069 words)

	Elkies trinomial curves - Wikipedia, the free encyclopedia
		In number theory, the Elkies trinomial curves are certain hyperelliptic curves constructed by Noam Elkies which have the property that rational points on them correspond to trinomial polynomials giving an extension of Q with particular Galois groups.
		The curve is a plane algebraic curve model for a Galois resolvent for the trinomial polynomial equation x
		The curve has genus two, and so by Faltings theorem there are only a finite number of rational points on it.
	en.wikipedia.org /wiki/Elkies_trinomial_curve (358 words)

	PSL(2,7) - Free net encyclopedia (Site not responding. Last check: 2007-10-18)
		In mathematics, the projective special linear group PSL(2,7) is a finite simple group that has important applications in algebra, geometry, and number theory.
		It is the automorphism group of the Klein quartic as well as the symmetry group of the Fano plane.
		With 168 elements PSL(2,7) is the second-smallest nonabelian simple group after the alternating group A
	www.netipedia.com /index.php/PSL(2,7) (641 words)

	How to Make the Mathieu Group M(24) (Site not responding. Last check: 2007-10-18)
		As it turns out, the group G(X) generated by {s,t} is isomorphic to both PSL(2,7) and GL(3,2), and these are isomorphic to each other.
		Describe how half of the pink triangles should be distinguished from the other half, based on the coloring of the tiling.
		The permutations s and t, given above, generate the symmetry group G(X) of the polyhedron X. Also recall that G(X) is isomorphic to PSL(2,7) and to GL(3,2), and that these are isomorphic to each other.
	homepages.wmich.edu /~drichter/mathieu.htm (1988 words)

	[No title]
		For example, PSL(2,5) turns out to be isomorphic to A_5, which acts on a set of 5 elements in an obvious way.
		PSL(2,7) and PSL(2,11) act on a 7-element set and an 11-element set, respectively, in sneaky ways which Kostant describes.
		A_5 is both PSL(2,5) and the subgroup of PSL(2,11) that fixes a point of an 11-element set.
	math.ucr.edu /home/baez/twf_ascii/week79 (2485 words)

	GAP Forum: Re: Help (Site not responding. Last check: 2007-10-18)
		The map you gave yesterday was onto SL(2,7), not PSL(2,7), and with the
		The value of the relator is not the identity in the image group.
		Roughly, you work out the map of G onto the regular permutation of PSL(2,7),
	www-groups.dcs.st-and.ac.uk /gap/ForumArchive/Holt.1/Derek.1/Re___Hel.1/1.html (193 words)

	GAP Manual: 1.26 About Group Libraries
		Instead of specifying a single value that a function must return you can simply specify a list of such values.
		gap> AllPrimitiveGroups(DegreeOperation, [1..10], > IsSimple, true, > IsCyclic, false); [ A(5), PSL(2,5), A(6), PSL(3,2), A(7), PSL(2,7), A(8), PSL(2,8), A(9), A(5), PSL(2,9), A(10) ]
		If selection functions would really run over the list of all groups in a group library and apply the function arguments to each of those, they would be very inefficient.
	www-groups.dcs.st-and.ac.uk /~gap/Gap3/Manual3/C001S026.htm (1617 words)

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