Structuralism and Group Theory

I just read Amir Aczel’s book on Bourbakis, The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed. In my opinion, the book was terribly written, but it did bring up a number of interesting topics. Chief among them was structuralism, which is a philosphy based upon the idea that there are symmetries and patterns inherent to each branch of knowledge. For example, linguists were able to decode the inherent structures in language by sorting and identifying patterns based on some assumptions and inductive reasoning about phonemes. Additionally, the author discussed how group theory was used by Claude Levi-Strauss and Andre Weil to sort out the structures in anthropological kinship studies.

Groups are used throughout mathematics and other sciences to descibe the internal symmetries within a problem. More specifically, an internal symmetry of a structure is usually associated with an invariant property, and the operations that preserve this invariant property make up the group. For example, a square has eight symmetry operations that preserve its structure: the identity operation; a 90º, a 180º, and a 270º rotation around the center of the square; a 180º rotation about each of the diagonals; and a 180º rotation around each of the axes that bisect two opposing sides. How such an abstract idea as group theory can be applied to practical problems is the subject of many texts.

There are a number of books that talk about how to apply group theory to physics and chemistry, but I haven’t found any for engineering. Does anyone have any ideas on where I can find a guide on to how to apply group theory to my engineering applications?