11. The companion concept to associated bundles is the "'reduction of the structure group "'of a G-bundle B. 12. The structure group is the orthogonal group. 13. If a structure group G is a complex semisimple matrix group, the configuration space of quantum gauge theory. 14. He graduated from a highly structured group home to one where he had more responsibility, then to independent living. 15. Instead, Lippman was part of a loosely structured group of young rebels unbeholden to any power, foreign or domestic. 16. Any two frames are related by an element in the subgroup of the structure group of preserving the trace form. 17. In general, this is possible for any " G "-connection on a fibre bundle with structure group " G ". 18. The company's Osaka Works provides many services for the Ship and Steel Structure group and other groups in the company. 19. They live in forests throughout Central and South America, congregating in hierarchically structured groups of maybe 25 to 35 individuals. 20. More generally, it can be used to denote the head of any hierarchically structured group of people, often as a compound word.
