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"Starting with matrices over the integers, part 1 of this book provides a measured introduction to such groups, two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in part 2 starting with matrices having polynomial entries, two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form."

"Dalam teori grup, terdapat teorema yang menyatakan bahwa suatu grup abelian berhingga dapat didekomposisi menjadi hasil kali langsung dari subgrup-subgrupnya. Karena order dari grup abelian berhingga dapat difaktorkan menjadi perkalian dari bilangan-bilangan prima, maka subgrup hasil dekomposisinya adalah grup siklik. Salah satu penggunaan dari hasil dekomposisi ini adalah menghitung order automorfisma grup abelian berhingga melalui perhitungan order automorfisma dari grup-grup hasil dekomposisinya. Dalam skripsi ini dibahas mengenai pembuktian dekomposisi grup abelian berhingga menjadi hasil kali langsung dari grup-grup siklik dan perhitungan order automorfisma dari grup abelian berhingga.

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In group theory, there is a theorem which states that a finite abelian group can be decomposed into a direct product of its subgroups. Since an order of the finite abelian group can be factored into product of prime numbers,then the resulting decomposition subgroups are cyclic groups. One of these applications of the theory is calculating the authomorphism order of a finite abelian group through calculation of automorphism order from the group as its decomposition result.This mini thesis discussed about the proof of finite abelian group into direct product of its cyclic groups and the calculation of its automorphism order from the finite abelian group."

"These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics, in particular model building beyond the standard model - non-Abelian discrete symmetries have been applied to understand the three-generation flavor structure in particular. This text explicitly introduces and studies the group-theoretical aspects of many concrete groups and shows how to derive conjugacy classes, characters, representations, and tensor products for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest."

"Matrix functions are of growing interest due to their fascinating theory and the many applications in which they provide insight and succinct solutions. Functions of Matrices: Theory and Computation gives a thorough treatment of the theory of matrix functions and numerical methods for computing them, as well as an overview of applications."

"This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity."