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	Ferdinand Georg Frobenius (Site not responding. Last check: 2007-11-06)
		In his work in group theory, Frobenius combined results from the theory of algebraic equations, geometry, and number theory, which led him to the study of abstract groups.
		Frobenius collaborated with Schur in representation theory of groups and character theory of groups.
		Among the topics which Frobenius studied towards the end of his career were positive and non-negative matrices.
	www.stetson.edu /~efriedma/periodictable/html/Fr.html (551 words)

	Frobenius (Site not responding. Last check: 2007-11-06)
		Frobenius was only in Berlin for a year before he went to Zürich to take up an appointment as an ordinary professor at the Eidgenössische Polytechnikum.
		Weierstrass, strongly believing that Frobenius was the right person to keep Berlin in the forefront of mathematics, used his considerable influence to have Frobenius appointed.
		Frobenius was the leading figure, on whom the fortunes of mathematics at Berlin university rested for 25 years.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Frobenius.html (1986 words)

	Frobenius-Perron equation (Site not responding. Last check: 2007-11-06)
		Frobenius, Nikolaj Forfatterprofil med biografi og lenker til artikler fra NRK.
		Frobenius, Nikolaj Forfatterprofil hos Aftenposten med biografi, lenker til artikler og anmeldelser.
		Nikolaj Frobenius: Der Anatom Man nehme ein paar literarische Versatzstücke, stöpsle sie mittels einer mehr oder weniger plausiblen Handlung zusammen und hoffe, dass das p.t.
	www.serebella.com /encyclopedia/article-Frobenius-Perron_equation.html (361 words)

	PlanetMath: Frobenius group
		In this case the Frobenius group is called non-regular.
		is called a Frobenius complement, and has the remarkable property that it is distinct from any conjugate by an element not in the subgroup.
		This is version 2 of Frobenius group, born on 2002-12-14, modified 2003-08-22.
	planetmath.org /encyclopedia/FrobeniusGroup.html (91 words)

	Search Results for Frobenius (Site not responding. Last check: 2007-11-06)
		Frobenius was somewhat critical of the area that Landau worked in, and remarked at times that Landau's work would cease to become important if the Riemann hypothesis were proved.
		Frobenius was one of his teachers and he was to greatly influence Schur and later to direct his doctoral studies.
		Frobenius used Young tableaux for the first time in 1903 when he investigated representations of the symmetric group but it was not until 1906 that Young learnt of Frobenius's applications of his methods.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Frobenius&CONTEXT=1 (3402 words)

	Frobenius, (Ferdinand) Georg - Hutchinson encyclopedia article about Frobenius, (Ferdinand) Georg
		Frobenius was born in Berlin and studied at Göttingen.
		He was professor at the Eidgenossische Polytechnikum in Zürich, Switzerland, 1875–92, and at Berlin for the rest of his career.
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	encyclopedia.farlex.com /Frobenius%2c+(Ferdinand)+Georg (176 words)

	PlanetMath: Frobenius morphism
		In this case the Frobenius map is an automorphism of
		Hence the Frobenius morphism is an endomorphism (or isogeny) of the elliptic curve.
		This is version 1 of Frobenius morphism, born on 2003-08-15.
	www.planetmath.org /encyclopedia/FrobeniusMorphism.html (130 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Frobenius generalized the theorem to irreducible non-negative matrices: G.
		Frobenius generalized the result to apply to nonnegative matrices, introducing the key notion of primitivity in 1912.
		There may have been some independent discovery since Frobenius was about 60 at the time and Perron appears to have been at an early stage of his career (I don't have any biographical data on him, but his book on Continued Fractions, published in 1929 claims to be based on lectures given in 1909).
	www.math.niu.edu /~rusin/known-math/00_incoming/perron_frob (477 words)

	CSDC : Frobenius Integrability and the Transition to Turbulence. (Site not responding. Last check: 2007-11-06)
		CSDC : Frobenius Integrability and the Transition to Turbulence.
		The decay of turbulence is a transition from a state where the Frobenius theorem is not satisfied to a state where the Frobeniou theorem is satisfied (and the flow is no longer turbulent).
		It is possible to demonstrate that the stremline flow generates a connected topology, while the non-streamline flow generates a non-connected topology.
	www22.pair.com /csdc/ed3/ed3fre18.htm (245 words)

	Activity on Frobenius manifolds, quantum cohomology, and singularities
		Frobenius manifolds are manifolds with a rich additional structure, a multiplication and a metric on the tangent bundle.
		Frobenius manifolds turn up in quantum cohomology, where they encode information of Gromov-Witten invariants of genus 0, and in singularity theory, as base spaces of unfoldings of singularities.
		Isomorphism of certain of the Frobenius manifolds on both sides is one version of mirror symmetry.
	www.mpim-bonn.mpg.de /html/services/activities/frobenius.html (578 words)

	► » properties of the Frobenius group (Site not responding. Last check: 2007-11-06)
		all Frobenius complements in G are conjugate to each other.
		A finite Frobenius group G with Frobenius complement H and corresponding
		Frobenius kernel N satisfied the above 6 properties.
	www.science-chat.org /properties-of-the-Frobenius-group-8690193.html (541 words)

	Nikolaj Frobenius (Site not responding. Last check: 2007-11-06)
		Nikolaj Frobenius er født i Oslo i 1965.
		Frobenius er utdannet ved filmlinjen på The London Institute og har skrevet flere filmmanuskripter, blant annet thrilleren Insomnia fra 1997, som senere ble nyinnspilt i Hollywood.
		Nikolaj Frobenius var redaktør for Vinduet i perioden 1998—2001 og bor i Oslo.
	www.bokportalen.no /vis_forfatter.asp?forfatter=518 (93 words)

	Geometry.Net - Scientists: Frobenius Georg
		Georg Frobenius lived from 1849 to 1917 Frobenius combined results from the theory of algebraic equations, geometry, and number theory, which led him to the study of abstract groups, the representation theory of groups and the character theory of groups.
		Ferdinand Georg frobenius georg Frobenius briefly attended the University of GÃ¶ttingen, but he only studied there for one semester before returning to the city of his birth, Berlin.
		Ferdinand georg frobenius Ferdinand georg frobenius was the first person after Gauss who made an extensive contribution to representation theory.
	www.geometry.net /detail/scientists/frobenius_georg.html (1129 words)

	Mette Frobenius booking
		Mette Frobenius er 33 år, uddannet erhvervsjurist på Handelshøjskolen med speciale i presseetik, men har siden 1993 levet af at underholde.
		Derudover er Mette Frobenius meget brugt som konferencier, når en hel dag skal kædes sammen af en skarp og underholdende vært.
		Mette Frobenius fortæller om den lidt bratte indføring i komikkens verden, og kommer med gode og praktiske råd om, hvordan man trænger bedre igennem i en større forsamling.
	www.lykkemusic.dk /VisKunstner.asp?id=204 (406 words)

	Atlas: Frobenius groups: it's all algebraic number theory by Ron Brown (Site not responding. Last check: 2007-11-06)
		Frobenius groups play a prominent role in the general theory of finite groups.
		We illustrate this with a very elementary construction of all Frobenius groups whose Frobenius complement is either the quaternion group or the special linear group SL(2,Z/5Z) and with some combinatorial results (e.g., a count of the metabelian Frobenius groups of order at most one million).
		The key idea is that Frobenius groups with abelian kernel correspond precisely to finite modules over certain well-behaved classical maximal orders, and the indecomposable modules correspond to powers of maximal ideals of the associated Dedekind domain.
	atlas-conferences.com /cgi-bin/abstract/cacv-07 (182 words)

	[No title]
		The usual way of thinking about K is to observe it's a group with a collection of fixed-point-free automorphisms on it, forming the group H. There are oodles of results describing groups which admit f-p-f automorphisms of various sorts.
		Kegel and B. Wehrfritz [Locally finite groups, North-Holland, Amsterdam, 1973; MR 57 #9848] showed that local finiteness is a sufficient hypothesis and gave an example of a strong failure of the theorem in the general case.
		In addition if (ii) holds, the Frobenius kernel is abelian; and if any three elements of $G$ generate a finite subgroup then the Frobenius kernel satisfies an Engel condition.
	www.math.niu.edu /~rusin/known-math/98/frob_ker (788 words)

	Read This: Pioneers of Representation Theory
		A chapter each is then alloted to the turn-of-the-century work of Frobenius and Burnside and an additional two chapters apiece are devoted to the later work of Schur and Brauer.
		Adolf Hurwitz's letter was an eye-opener for Frobenius, as he had associated Hurwitz with the mathematical school of Felix Klein at Gottingen.
		Frobenius was skeptical of the big-picture geometric approach of Klein, and his reply to Hurwitz, in a letter dated 3 February 1896, contains the passage:
	www.maa.org /reviews/pioneers.html (1223 words)

	Frobenius Series Solution of O.D.E.'s
		Frobenius series can be used to solve differential equations at a regular singular point.
		The parameter r must be chosen so that when the series is substituted into the D.E. the coefficient of the smallest power of x is zero.
		Observe that the coefficients that involve c[1] are that multiple of the first Frobenius solution.
	math.fullerton.edu /mathews/N310/projects3/p22.htm (674 words)

	Frobenius
		In 1909 the immigrant German organ builder Theodor Frobenius (1885-1972) established his organ-building firm in Copenhagen.
		Because of his eminent talents as an artist and craftsman he soon made a name for himself in church circles.
		In 1944 the sons Walther and Erik Frobenius entered the business and at about the same time the firm began to build organs according to classical principles with mechanical action and slider wind-chests.
	www.musikhistoriskmuseum.dk /reg/frobeniusx.htm (140 words)

	Frobenius gruppe (Site not responding. Last check: 2007-11-06)
		frobenius gruppe any of those with fur on the way content you, I cry did the harbour What will become before he it with a dense low forest.
		Madelon in the presence of the problems devoid of worthy too prayse that, whiche whose thoughts, have carried Empedocles frobenius gruppe of battle, terrible and vocal music.
		As one of its as an "inner question of his life, hee hath better remedy than in music through the clangs when the light, are, when
	frobenius-gruppe.parvo.nl (128 words)

	The Frobenius Page (Site not responding. Last check: 2007-11-06)
		The Frobenius Page: A collection of one-liners and pithy sayings about Frobenius, as a guide to the perplexed about this most mysterious of operators (especially myself).
		The kernels of Frobenius and its iterates give natural infinitesimal neighborhoods of the identity on group schemes.
		Frobenius liftings to characteristic zero - p-adic analogs of Kahler metrics (Mochizuki).
	www.ma.utexas.edu /~benzvi/math/frobenius.html (379 words)

	Citebase - Frobenius properties and Maschke-type theorems for entwined modules
		Frobenius properties and Maschke-type theorems for entwined modules
		In this paper, Frobenius properties and Maschke-type theorems, known for Doi-Hopf modules are extended to the case of entwined modules.
		We present a unified apoach to the study of separable and Frobenius algebras.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:math/9806025 (699 words)

	References for Frobenius (Site not responding. Last check: 2007-11-06)
		R Haubrich, Frobenius, Schur, and the Berlin algebraic tradition, in Mathematics in Berlin (Berlin, 1998), 83-96.
		K Miyake, A note on the arithmetic background to Frobenius' theory of group characters, Exposition.
		F L Williams, History and variations on the theme of the Frobenius reciprocity theorem, The Mathematical Intelligencer 13 (3) (1991), 68-71.
	www-gap.dcs.st-and.ac.uk /~history/References/Frobenius.html (156 words)

	NRK.no - Forfattere (Site not responding. Last check: 2007-11-06)
		I 1999 utga Nikolaj Frobenius romanen ”Den sjenerte pornografen”.
		Jostein Gaarder og Nikolaj Frobenius fortel på kvar sitt vis korleis historier - sanne som oppdikta - grip inn i livet og gjer det vanskeleg å leve.
		Nikolaj Frobenius er fra Oslo og debuterte i 1986.
	www.nrk.no /nyheter/kultur/forfattere/1366228.html?p_saksunivers_id=2820 (272 words)

	Geometry.Net - Scientists: Frobenius Georg
		Extractions: poka¿ powi±zane Frobenius Georg Ferdinand (1849-1917), matematyk niemiecki.
		Extractions: R Haubrich, Frobenius, Schur, and the Berlin algebraic tradition, in Mathematics in Berlin (Berlin, 1998), 83-96.
		N Stuloff, G F Frobenius, Neue Deutsche Biographie V F L Williams, History and variation on the theme of the Frobenius reciprocity theorem, The Mathematical Intelligencer Main index Birthplace Maps Biographies Index
	www.geometry.net /scientists/frobenius_georg.php (1071 words)

	The Frobenius and Monodromy operators for Curves and Abelian Varieties, by Robert Coleman and Adrian Iovita (Site not responding. Last check: 2007-11-06)
		The Frobenius and Monodromy operators for Curves and Abelian Varieties, by Robert Coleman and Adrian Iovita
		In this paper, we give explicit descriptions of Hyodo and Kato's Frobenius and Monodromy operators on the first $p$-adic de Rham cohomology groups of curves and Abelian varieties with semi-stable reduction over local fields of mixed characteristic.
		This paper was motivated by the first author's paper "A $p$-adic Shimura isomorphism and periods of modular forms," where conjectural definitions of these operators for curves with semi-stable reduction were given.
	www.math.uiuc.edu /Algebraic-Number-Theory/0054 (100 words)

	IngentaConnect Frobenius Groups Generated by Quadratic Elements (Site not responding. Last check: 2007-11-06)
		It is proved that a Frobenius group generated by two quadratic elements is finite and its core is commutative.
		In particular, any Frobenius group generated by two elements of order at most 4 is finite.
		The results mentioned are used to show that a group G acting freely on an Abelian group is finite if it is generated by elements of order 3, and the order of a product of every two elements of order 3 in G is finite.
	api.ingentaconnect.com /content/klu/allo/2003/00000042/00000003/00469353 (201 words)

	Frobenius Series Solution of a D. E.
		Caveat: There are some instances when only one Frobenius solution can be constructed.
		Use Frobenius series to solve the D. Solution 2.
		Use Frobenius series to solve the D. A solution is known to be the celebrated
	math.fullerton.edu /mathews/n2003/FrobeniusSeriesMod.html (373 words)

	WAGS-Spring 2003: Abstracts (Site not responding. Last check: 2007-11-06)
		A family of Frobenius modules is an abstraction based on the small quantum multiplication by elements of H^{1,1} on the cohomology of a Calabi-Yau manifold.
		In general, there is a correspondence between maximally degenerating polarized variations of Hodge structure and families of Frobenius modules.
		The talk presents a formula computing the number of curves of a given genus and degree through a collection of generic points in a toric surface (both over complex and real numbers).
	math.stanford.edu /%7Eazinger/wags03sp/abstracts.html (346 words)

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