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	Sylow biography
		In 1862 Sylow lectured at the University of Christiania, substituting for Broch.
		Sylow proved what is perhaps the most profound result in the theory of finite groups.
		Sylow became an editor of Acta Mathematica and, in 1894, he was awarded an honorary doctorate from the university of Copenhagen.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Sylow.html (478 words)

	Sylow theorem - Wikipedia, the free encyclopedia
		The Sylow theorems of group theory, named after Ludwig Sylow, form a partial converse to Lagrange's theorem, which states that if H is a subgroup of a finite group G, then the order of H divides the order of G.
		Let p be a prime number; then we define a Sylow p-subgroup of G to be a maximal p-subgroup of G (i.e., a subgroup which is a p-group, and which is not a proper subgroup of any other p-subgroup of G).
		Theorem 2: All Sylow p-subgroups of G are conjugate to each other (and therefore isomorphic), i.e.
	en.wikipedia.org /wiki/Sylow_theorem (1068 words)

	Encyclopedia: Group theory (Site not responding. Last check: 2007-10-29)
		In abstract algebra, for a number of algebraic structures, the fundamental theorem on homomorphisms relates the structure of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism.
		In mathematics, most commonly, Lagranges theorem states that if G is a finite group and H is a subgroup of G, then the order (that is, the number of elements) of H divides the order of G. This can be shown using the concept of left cosets of H...
		The Sylow theorems of group theory, named after Ludwig Sylow, form a partial converse to Lagranges theorem, which states that if H is a subgroup of a finite group G, then the order of H divides the order of G. The Sylow theorems guarantee, for certain divisors of the...
	www.nationmaster.com /encyclopedia/Group-theory (3569 words)

	Third Sylow Theorem (Site not responding. Last check: 2007-10-29)
		By the second Sylow theorem, the action of conjugation on sylow subgroups is transitive.
		The size of the orbit is the index of the stabilizer of h in g, and since the action is conjugation, the stabilizer is the normalizer, which is a subgroup somewhere between h and g.
		The sylow subgroup j is fixed by h iff yj/y = j for all y in h, iff h is contained in the normalizer of j.
	www.mathreference.com /grp-act,sylow3.html (391 words)

	PlanetMath: Sylow theorems, proof of
		Proposition 3 The intersection of a Sylow p-subgroup with the normalizer of a Sylow p-subgroup is the intersection of the subgroups.
		By the orbit-stabilizer theorem, the size of an orbit is the index of the stabilizer, and under this action the stabilizer of any
		This is version 6 of proof of Sylow theorems, born on 2002-07-22, modified 2005-07-11.
	planetmath.org /encyclopedia/ProofOfSylowTheorems.html (437 words)

	[No title]
		Mathematicians were not immune, and at a mathematics conference in July, 1999, Paul and Jack Abad presented their list of "The Hundred Greatest Theorems." Their ranking is based on the following criteria: "the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result."
		The list is of course as arbitrary as the movie and book list, but the theorems here are all certainly worthy results.
		Liouville’s Theorem and the Construction of Trancendental Numbers
	personal.stevens.edu /~nkahl/Top100Theorems.html (217 words)

	Sylow theorem - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-29)
		The following facts were first proposed and proven by Norwegian mathematician Ludwig Sylow in 1872, and published in Mathematische Annalen.
		The proofs of the Sylow theorem exploit the notion of group action in various creative ways.
		The group G acts on itself or on the set of its p subgroups in various ways, and each such action can be exploited to prove one of the Sylow theorem.
	encyclopedia.worldsearch.com /sylow_subgroup.htm (1341 words)

	Sylow theorem (Site not responding. Last check: 2007-10-29)
		The Sylow theorems of group theory,named after Ludwig Sylow, form a partialconverse to the theorem of Lagrange, which states that ifH is a subgroup of a finite group G, then the order of Hdivides the order of G.
		All Sylow p-subgroups of G are conjugate toeach other (and therefore isomorphic), i.e.
		The proofs of the Sylow theorem exploit the notion of group action invarious creative ways.
	www.therfcc.org /sylow-theorem-210812.html (1264 words)

	MA3131 Group Theory
		The emphasis is on structure theorems, classification results and decomposition concepts that have evolved as a result of attempts to describe all possible groups.
		The module is designed to present a broad outline of the classification, to explain its significance, and to give a hint of the complexity of its proof.
		Sylow subgroups of finite groups; the Sylow theorems; characteristic subgroups; simple groups; normal and subnormal series; composition series and chief series; the Jordan-Hölder Theorem; solvable and nilpotent groups; commutator subgroups; upper and lower central series; derived series; that a finite
	www.mcs.le.ac.uk /Modules/MA-02-03/MA3131.html (691 words)

	Sylow theorem - Term Explanation on IndexSuche.Com
		of group theory, named after Ludwig Sylow, form a partial converse to the theorem_of_Lagrange, which states that if ''H'' is a subgroup of a finite group ''G'', then the order of ''H'' divides the order of ''G''.
		Let ''p'' be a prime_number; then we define a Sylow ''p''-subgroup of ''G'' to be a maximal ''p''-subgroup of ''G'' (i.e., a subgroup which is a ''p''-group, and which is not a proper subgroup of any other ''p''-subgroup of ''G'').
		The proofs of the Sylow theorem exploit the notion of group_action in various creative ways.
	www.indexsuche.com /Sylow_theorem.html (1499 words)

	Sylow theorem (Site not responding. Last check: 2007-10-29)
		The Sylow theorems guarantee for certain of the order of G the existence of corresponding subgroups and information about the number of those subgroups.
		Let p be a prime number ; then we define a Sylow p -subgroup of G to be a maximal p -subgroup of G (i.e.
		All Sylow p -subgroups of G are conjugate to each other (and therefore isomorphic) i.e.
	www.freeglossary.com /Sylow_subgroup (1607 words)

	Peter Ludwig Mejdell Sylow (Site not responding. Last check: 2007-10-29)
		Peter Ludwig Mejdell Sylow (12 December 1832 — 7 September 1918) was a Norwegian mathematician who proved foundational results in group theory.
		He was a substitute lecturer at University in 1862 covering Galois theory ; he posed then the question that to lead to the Sylow subgroups and his theorems about them.
		Subsequently he was an editor of Abel ’s papers with Sophus Lie.
	www.freeglossary.com /Ludwig_Sylow (192 words)

	The second and third Sylow Theorems
		This is the content of the second Sylow Theorem.
		This together with Theorem 10.1.2 establishes the claim.
		is non-trivial (by Theorem 4.3.5) and is, of course, abelian.
	web.usna.navy.mil /~wdj/tonybook/gpthry/node56.html (388 words)

	Useful Theorems
		An example of how this theorem can be useful is to look at a group
		Sylow's Theorem says there there is a subgroup
		Theorem 0.7 If P = k-1 and P is a p-cycle then
	www-math.cudenver.edu /~rrosterm/simple/node2.html (315 words)

	MA30110 - GROUP THEORY
		The concept of a group occurs naturally in situations involving symmetry or in which some quantity is being preserved; for example, various letters such as A, S and I possess different numbers of symmetries and rigid motions preserve distance.
		The principal structure theorems for finite groups will be described and applied in a variety of group theoretic contexts.
		To provide a deeper understanding of the concepts and techniques of abstract algebra, introduced in module MA20310, by focusing on the group concept, starting with an axiomatic development of group theory, establishing a structure theory, mainly in the context of finite groups, and giving brief illustrations of a selection of applications of group theory.
	www.aber.ac.uk /modules/current/MA30110.html (336 words)

	Conjugacy (Site not responding. Last check: 2007-10-29)
		Conjugacy and Sylow Theorems - Gallian, Ch 24 # 4,5, Fraleigh,...
		Regular conjugacy classes in the Weyl group and integrable hierarchies...
		CENTRAL AND LOCAL LIMIT THEOREMS FOR EXCEDANCES BY...
	www.scienceoxygen.com /math/267.html (198 words)

	Holder (Site not responding. Last check: 2007-10-29)
		Hölder clarifies the concept which he claims is neither new nor difficult but is not sufficiently appreciated.
		Hölder proved the uniqueness of the factor groups in a composition series, the theorem now called the Jordan-Hölder theorem.
		His methods use the Sylow theorems in a similar way to how the problem would be solved today.
	www-history.mcs.st-andrews.ac.uk /Mathematicians/Holder.html (482 words)

	Sylow's theorems
		(c) The number of Sylow p-subgroups of G divides the order of G and is equal to 1 modulo p.
		By part (b) we know that if G acts by conjugation on S, the action is transitive, that is, there is one orbit only.
		The number of Sylow p-subgroups is the length of the orbit, which in turn divides the order of G.
	www.pitt.edu /~gmc/ch1/node6.html (521 words)

	Read This: Briefly Noted, April 2005
		The first six chapters deal with groups: basic definitions, examples, the Sylow theorems, group actions, and a variety of related topics.
		The reviewer thinks that the authors have done a fantastic job choosing the problems, which are perfectly arranged so the students can progressively move on from topic to topic, discovering on their own the proofs of the most well-known results and applications.
		The authors present the Weiner-Ikehara approach to the Prime Number Theorem, along with generalizations that lead to the asymptotic formula for number of sums of two squares.
	www.maa.org /reviews/brief_apr05.html (2251 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Course Content: (time constraints are approximate): Group, subgroups, Lagrange's Theorem, normal subgroups, factor groups, and the Isomorphism and Correspondence Theorems.
		[6 days] The Sylow Theorems with applications to simple groups (one may choose to prove the classification of finite abelian groups through the Sylow Theorems).
		Sample Grading and Evaluation Procedures A graduate student is expected to creatively engage the mathematical material of the course.
	www.auburn.edu /~smith01/txtsyll/syl7310.txt (617 words)

	BEACHY / BLAIR: ABSTRACT ALGEBRA
		The final three chapters (on the structure of groups, Galois theory, and unique factorization) are written at a more demanding level, consistent with material usually considered to be at an undergraduate/graduate level.
		Includes such optional topics as finite fields, the Sylow theorems, finite abelian groups, the simplicity of PSL(2,F), Euclidean domains, unique factorization domains, cyclotomic polynomials, arithmetic functions, Moebius inversion, quadratic reciprocity, primitive roots, and diophantine equations.
		In fact, this is the last of a thread of number theoretic applications that run through the text, including a proof of the quadratic reciprocity law in Section 6.7 and a study of primitive roots modulo p in Section 7.5.
	www.math.niu.edu /~beachy/abstract_algebra_2ed (1861 words)

	Category.org - The Online Shopping Center: Books - Group Theory (Site not responding. Last check: 2007-10-29)
		The fact that he states the heart of Galois Theory (the Fundamental Theorem of Galois Theory) right at the beginning is, in my opinion, essential in the theory's presentation.
		The second section (chapters 6-13) gives a more graduate level presentation of the material.Starting with a discussion of group algebras, moving onto inducted representations Artin's theorem (the existence of virtual characters) The third section is Brauer Theory.
		For an average engineer without too much mathematical background this may be a bit too much, but the chapter is well written and provides usefull information that is used in chapter 4 to derive the irreducible representations and character tables for the point groups discussed in chapter 2.
	www.category.org /browse/books/13940/index.html (5868 words)

	MAS305, Algebraic Structures II (Site not responding. Last check: 2007-10-29)
		The group theory portion includes the basics of group actions, finite p-groups, Sylow theorems and applications, and the Jordan-Holder theorem.
		Group theory: group actions; finite p-groups; Sylow theorems and applications; Jordan-Holder theorem; finite soluble groups.
		Modules: foundations of module theory; isomorphism theorems; structure of finitely generated modules over Euclidean domains.
	www.maths.qmw.ac.uk /~sharon/courses/MAS305.html (145 words)

	BEACHY/BLAIR: ABSTRACT ALGEBRA
		Includes such optional topics as finite fields, the Sylow theorems, finite abelian groups, the simplicity of PSL(2,F), Euclidean domains, unique factorization domains, cyclotomic polynomials, arithmetic functions, Moebius inversion, quadratic reciprocity, primitive roots, and diophantine equations.
		As a number theoretic application, we present a proof of Fermat's last theorem for the exponent 3.
		In fact, this is the last of a thread of number theoretic applications that run through the text, including a proof of the quadratic reciprocity law in Section 6.7 and a study of primitive roots modulo p in Section 7.5.
	home.att.net /~jabeachy/order.htm (1770 words)

	Math 404
		W 4/13 - I finished the main theorem on solvability.
		F 4/22 - I finished examples and began the proof of Sylow 1.
		M 4/25 - I finished Sylow 1 and Sylow 2.
	www.math.umd.edu /~rah/m404syl.html (473 words)

	The Sylow Theorems (Site not responding. Last check: 2007-10-29)
		We have already observed (see statements after the proof of Theorem 6.2; also see Exercise 4 for Section 6.2) that the converse of Lagrange's theorem is false, i.e., if
		These theorems constitute the Sylow Theorems which, along with a few applications, will be the matter of concern of this chapter.
		Existence of Sylow subgroups; the first Sylow Theorem
	web.usna.navy.mil /~wdj/tonybook/gpthry/node53.html (81 words)

	Wash U Graduate Program : Graduate Course Offerings
		The emphasis is on proving theorems, not on calculation techniques or applications of calculus to other quantitative disciplines.
		Prerequisites: We shall refer to theorems from advanced calculus at the level of Math 411 and Math 412, and linear algebra at the level of Math 309.
		This course covers complex tori and their line bundles, Appel-Humbert Theorem, Theta functions and Theta groups, addition formula and multiplication formula for Theta functions, embeddings of abelian varieties into projective spaces via Theta functions, and moduli spaces of abelian varieties.
	www.math.wustl.edu /academics/graduate/courses.html (2228 words)

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