This book provides a modern introduction to the representation theory of finite groups. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all ...
"A Concise Introduction to Pure Mathematics, Second Edition" provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ...
With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a ...
Since the 1980s, the theory of groups - in particular simple groups, finite and algebraic - has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent ...
In this paper, we complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small. A number of ...
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