A Hall subgroup of G is a subgroup whose order is a Hall divisor of the order of G. In other words, it is a subgroup whose order is coprime to its index.
If π is a set of primes, then a Hall π-subgroup is a subgroup whose order is a product of primes in π, and whose index is not divisible by any primes in π.
Read more about Hall Subgroup: Examples, Hall's Theorem, A Converse To Hall's Theorem, Sylow Systems, Normal Hall Subgroups
Famous quotes containing the word hall:
“I may be able to spot arrowheads on the desert but a refrigerator is a jungle in which I am easily lost. My wife, however, will unerringly point out that the cheese or the leftover roast is hiding right in front of my eyes. Hundreds of such experiences convince me that men and women often inhabit quite different visual worlds. These are differences which cannot be attributed to variations in visual acuity. Man and women simply have learned to use their eyes in very different ways.”
—Edward T. Hall (b. 1914)