About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 45. Chapters: Abelian group, Cyclic group, Simple group, List of group theory topics, Free group, Dihedral group, Solvable group, Nilpotent group, Hamiltonian group, SQ universal group, Triangle group, Free abelian group, Word metric, Hyperbolic group, Algebraically closed group, Perfect group, A-group, Z-group, Divisible group, Algebraic group, Finite group, Subdirectly irreducible algebra, CA group, Artin group, Powerful p-group, Locally finite group, Complemented group, Complete group, Polycyclic group, Automatic group, Supersolvable group, Residually finite group, CN group, Slender group, Superperfect group, Quasisimple group, Imperfect group, Almost simple group, Monomial group, Metabelian group, Thin group, Iwasawa group, Semisimple algebraic group, Nonabelian group, Characteristically simple group, Arithmetic group, Parafree group, Cotorsion group, Metacyclic group, Residual property, T-group, Algebraically compact group, Metanilpotent group, Triple product property, Absolutely simple group, FC-group, Critical group, Almost perfect group, Strictly simple group, HN group, Capable group, Representation rigid group. Excerpt: In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order (the axiom of commutativity). Abelian groups generalize the arithmetic of addition of integers. They are named after Niels Henrik Abel. The concept of an abelian group is one of the first concepts encountered in undergraduate abstract algebra, with many other basic objects, such as a module and a vector space, being its refinements. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood. On the other hand, the theory of infinite ab...
