Inhaltsangabe
Excerpt from Primitive Groups, Vol. 1
Some knowledge of Algebraic Numbers and of the ordinary Theory of Numbers is assumed to have been acquired by the reader by way of preparation for a serious study of the subject of which this volume treats.
An apology may be in order for the arrangement of the subject matter. It was arranged as it is to meet the needs of actual instruction. The use of group characteristics, as developed by Frobenius, should be a familiar tool in the hands of the student as early as possible. There fore linear substitutions are taken up in the third chapter. From the point of view of strict logic this study of linear substitutions and of linear groups should be quite fully developed before those very special substitutions which we call permutations are considered. But the idea of groups of non-commutative Operations can, in the author's opinion, be best gained from a few lessons on the concrete and familiar permuta tions of a finite number of letters. Therefore the first two chapters are intended to familiarize the learner with the simpler processes used in Group Theory, to exhibit the fundamental theorems which admit of briefly worded proof, and to prepare the way for the more difficult developments of linear groups. Moreover, since any abstract group of finite order is isomorphic to some group of permutations, it would seem that sufficient generality can be attained if the phraseology of the abstract theory is ignored, as is done in this book.
In talking of prime numbers it is admitted that it is a matter of in difference whether unity is included among the primes or not. May one be permitted the same license, if for the sake of convenience in stating certain theorems, the identical substitution alone is denied the dignity of being called a group The new terms Similar groups.
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Paperback. Zustand: New. Print on Demand. This book delves into the foundations of group theory, an abstract branch of mathematics that explores sets of elements and their combinations. It begins by introducing the fundamental principles, such as permutations, group elements, and the concept of group order and degree. The author provides a detailed examination of transitive groups and their subgroups, leading to the development of crucial theorems like Lagrange's theorem and Sylow's theorem. Through the study of invariant subgroups and homomorphisms, the book explores the interplay between different group structures. It concludes with a discussion of complete groups, offering valuable insights into the nature of groups and their applications in mathematics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781332331604_0
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