Actions of Groups: A Second Course in Algebra

This course builds on the foundations of modern algebra by exploring group actions, which reveal the deeper structure of groups and their applications to topics such as polynomial equations and the classification of finite simple groups. Active learning modules and review chapters support students in transitioning to a deeper understanding of these concepts.

Format: Paperback / softback
Length: 226 pages
Publication date: 05 January 2023
Publisher: Cambridge University Press

This second course in modern algebra delves into the intricate algebraic tools required to explore profound topics that were only hinted at in a first course. By utilizing the unifying concept of group actions, students gain a deeper understanding of the mathematical structures necessary to classify finite simple groups, comprehend the role of groups in solving polynomial equations, and unravel the underlying complexities of groups.

From the perspective of permutations of a set, linear transformations on a vector space, or automorphisms of a field, the deeper structure of a group becomes apparent. This allows for the distinction between two different groups or the demonstration of the solvability of a polynomial equation through radicals. By developing the properties of these group actions, students encounter essential algebraic concepts such as the Sylow theorems and their applications, Galois theory, and representation theory.

To facilitate a smooth transition into this advanced level of study, the course includes warmup chapters that review and build upon the foundational concepts of the first course. Additionally, interactive learning modules are designed to engage students actively in the learning process, helping them grasp the complexities of modern algebra and develop a deeper understanding of the subject matter.

Weight: 362g
ISBN-13: 9781009158114