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A detailed analysis of the internal structure of finite groups is a formidable challenge. What can be said about an arbitrary group? The idea is to look within G for subgroups from which the whole of G can be reconstructed. Quotient structures are an unfailingly effective tool for this purpose.
In a board game, it is fairly common, partway through a match, to feel that you are ahead of (or behind) your opponent. Through the example of Domineering, this article invites you to discover how John Conway formalized this notion.
Because Augustin-Louis Cauchy did not take a direct interest in solving algebraic equations, he is an overlooked figure in the history of group theory. Yet his research on permutations provided valuable tools for those who worked on Galois theory.
