Encyclopaedia Britannica, 11th Edition, "Groups, Theory of" to "Gwyniad": Volume 12, Slice 6

"Encyclopaedia Britannica, 11th Edition, 'Groups, Theory of' to 'Gwyniad'" by Various is a scientific publication written during the early 20th century. This segment of the encyclopaedia delves into the mathematical concept of groups, presenting a detailed examination of group theory, including definitions, operations, and particular characteristics of both continuous and discontinuous groups. At the start of this volume, the focus is on establishing the foundational concepts of group theory. It begins by defining a group as a set of operations that can be performed on a set of objects, highlighting the relationship between operations and their inverses, and introduces key terms such as subgroups and conjugate operations. The definitions are accompanied by algebraic notation and examples, transitioning seamlessly into discourse on various types of groups, including finite and infinite groups, ultimately setting the stage for more intricate discussions of specific groups and their mathematical implications.