Symmetry Groups and Their Applications
by Willard Miller
Publisher: Academic Press 1972
This is a beginning graduate level textbook on applied group theory. Only those aspects of group theory are treated which are useful in the physical sciences, but the mathematical apparatus underlying the applications is presented with a high degree of rigor.
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by W. B. V. Kandasamy, F. Smarandache, M. K. Chetry - arXiv
This book defines new classes of groupoids, like matrix groupoid, polynomial groupoid, interval groupoid, and polynomial groupoid. This book introduces 77 new definitions substantiated and described by 426 examples and 150 theorems.
by Alexander Kirillov, Jr. - SUNY at Stony Brook
The book covers the basic contemporary theory of Lie groups and Lie algebras. This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style.
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A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
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We review a number of methods for finding a finite algebra with a given congruence lattice, including searching for intervals in subgroup lattices. We also consider methods for proving that algebras with a given congruence lattice exist...