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Basic Abstract Algebra
This book provides a complete abstract algebra course, enabling instructors to select the topics for use in individual classes.
A Course in the Theory of Groups
"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." —-ACTA SCIENTIARUM MATHEMATICARUM
N-Algebraic Structures
In this book, for the first time we introduce the notions of N-groups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. The book is organized into six chapters. The first chapter gives the basic notions of S-semigroups, S-groupoids and S-loops thereby making the book self-contained. Chapter two introduces N-groups and their Smarandache analogues. In chapter three, N-loops and Smarandache N-loops are introduced and analyzed. Chapter four defines N-groupoids and S-N-groupoids. Since the N-semigroup structures are sandwiched between groups and groupoids, the study can be carried out without any difficulty. Mixed N-algebraic structures and S-mixed algebraic st...
The Mathematician Sophus Lie
Sophus Lie (1842-1899) is one of Norways greatest scientific talents. His mathematical works have made him famous around the world no less than Niels Henrik Abel. The terms "Lie groups" and "Lie algebra" are part of the standard mathematical vocabulary. In his comprehensive biography the author Arild Stubhaug introduces us to both the person Sophus Lie and his time. We follow him through: childhood at the vicarage in Nordfjordeid; his youthful years in Moss; education in Christiania; travels in Europe; and learn about his contacts with the leading mathematicians of his time.
Products of Finite Groups
The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups. Some of the topics covered by this book include groups whose subnormal subgroups are normal, permutable, or Sylow-permutable, products of nilpotent groups, and an exhaustive structural study of totally and mutually permutable products of finite groups and their relation with classes of groups. This monograph is mainly addressed to graduate students and senior researchers interested in the study of products and permutability of finite groups. A background in finite group theory and a basic knowledge of representation theory and classes of groups is recommended to follow it.
Representation Theory and Higher Algebraic K-Theory
Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of grou
Overgroups of Sylow Subgroups in Sporadic Groups
The maximal overgroups of noncyclic Sylow subgroups of the sporadic finite simple groups are determined. Moreover a geometric structure is associated to this collection of overgroups, which is useful in the study of sporadic groups.
Algebraic Patching
Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.
Séminaire de Théorie Des Nombres
Le travail ci-dessous developpe sur quelques points les tex:tes fondamentaux de C.L. Siegel [13[ et de K. Ramachandra [2). Remerclements C'est au Max Planck Institut de Bonn que la plus grande part des resultats (th. 2 et 3, ex:ception faite du point 3 d et th. 4 et 5) ont ete soit rectiges soit con~s. La rectaction definitive de ce travail a eu lieu ä l'Institut Fourier de Grenoble durant l'hiver 1990. Le th. 1 tel qu'il apparait ici, et le corollaire du th. 6 cf. identite (13), sont nouveaux. On trouvera une rectaction detailleedes th. 2 et 3 dans [51 et, parmi d'autres resultats, des th. 4, 5 et 6 dans [7). Que tous mes collegues et les deux equipes de secretartat recoivent ici mes remerciements les plus chaleureux. 2 1) On pose e( x) = e 1rix, x E C. Pour L un reseau complex:e, on note une base positivement olientee de L = lw + lw c'est-ä-dire teile que 1 2 On definit alors une forme modulaire .,.p> de poids 1 par 1](2)(w) ~fn (21l"i)ql/12 IJ ( - qn)2 1 { w2 n>l 1 12 q = e(W) , q 1 = e(W/12) , W = wt!w2 .
