Number of Simple Modules
In ordinary representation theory, the number of simple modules k(G) is equal to the number of conjugacy classes of G. In the modular case, the number l(G) of simple modules is equal to the number of conjugacy classes whose elements have order coprime to the relevant prime p, the so-called p-regular classes.
Read more about this topic: Modular Representation Theory
Famous quotes containing the words number of, number and/or simple:
“Even in ordinary speech we call a person unreasonable whose outlook is narrow, who is conscious of one thing only at a time, and who is consequently the prey of his own caprice, whilst we describe a person as reasonable whose outlook is comprehensive, who is capable of looking at more than one side of a question and of grasping a number of details as parts of a whole.”
—G. Dawes Hicks (1862–1941)
“Not too many years ago, a child’s experience was limited by how far he or she could ride a bicycle or by the physical boundaries that parents set. Today ... the real boundaries of a child’s life are set more by the number of available cable channels and videotapes, by the simulated reality of videogames, by the number of megabytes of memory in the home computer. Now kids can go anywhere, as long as they stay inside the electronic bubble.”
—Richard Louv (20th century)
“No author, without a trial, can conceive of the difficulty of writing a romance about a country where there is no shadow, no antiquity, no mystery, no picturesque and gloomy wrong, nor anything but a commonplace prosperity, in broad and simple daylight, as is happily the case with my dear native land.”
—Nathaniel Hawthorne (1804–1864)