Elements of Group Theory
by F. J. Yndurain
Publisher: arXiv 2007
Number of pages: 65
The following notes are the basis for a graduate course. They are oriented towards the application of group theory to particle physics, although some of it can be used for general quantum mechanics. They have no pretense of mathematical rigor.
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by E. Lee Lady - University of Hawaii
Contents: Modules Over Commutative Rings; Fundamentals; Rank-one Modules and Types; Quasi-Homomorphisms; The t-Socle and t-Radical; Butler Modules; Splitting Rings and Splitting Fields; Torsion Free Rings; Quotient Divisible Modules; etc.
by J. S. Milne
Contents: Basic Definitions and Results; Free Groups and Presentations; Coxeter Groups; Automorphisms and Extensions; Groups Acting on Sets; The Sylow Theorems; Subnormal Series; Solvable and Nilpotent Groups; Representations of Finite Groups.
by W. B. V. Kandasamy, F. Smarandache, M. K. Chetry - arXiv
This book defines new classes of groupoids, like matrix groupoid, polynomial groupoid, interval groupoid, and polynomial groupoid. This book introduces 77 new definitions substantiated and described by 426 examples and 150 theorems.
by W. B. Vasantha Kandasamy - American Research Press
The Smarandache semigroups exhibit properties of both a group and a semigroup simultaneously. This book assumes the reader to have a good background on group theory; we give some recollection about groups and some of its properties for reference.