1.

Record Nr.

UNINA9910508476403321

Autore

Davvaz Bijan

Titolo

A First Course in Group Theory / / by Bijan Davvaz

Pubbl/distr/stampa

Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2021

ISBN

981-16-6365-3

Edizione

[1st ed. 2021.]

Descrizione fisica

1 online resource (300 pages)

Collana

Mathematics and Statistics Series

Disciplina

512.2

Soggetti

Group theory

Number theory

Algebras, Linear

Group Theory and Generalizations

Number Theory

Linear Algebra

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Preliminaries Notions -- Symmetries of Shapes -- Binary Operations -- Cyclic Groups -- Inverse Functions and Permutations -- Group of Arithmetical Functions -- Matrix Groups -- Translation and Scaling Matrices -- Cosets of Subgroups and Lagrange’s Theorem -- Normal Subgroups and Factor Groups -- Some Special Subgroups -- Commutators and Derived Subgroups -- Maximal Subgroups -- Group Homomorphisms -- Homomorphisms and Their Properties -- Cayley’s Theorem -- Another View of Linear Groups.

Sommario/riassunto

This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. Topics on important examples of groups (like cyclic groups, permutation groups, group of arithmetical functions, matrix groups and linear groups), Lagrange’s theorem, normal subgroups, factor groups, derived subgroup, homomorphism, isomorphism and automorphism of groups have been discussed in depth. Covering all major topics, this book is targeted to undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the



reader.