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:
“Having children can smooth the relationship, too. Mother and daughter are now equals. That is hard to imagine, even harder to accept, for among other things, it means realizing that your own mother felt this way, too—unsure of herself, weak in the knees, terrified about what in the world to do with you. It means accepting that she was tired, inept, sometimes stupid; that she, too, sat in the dark at 2:00 A.M. with a child shrieking across the hall and no clue to the child’s trouble.”
—Anna Quindlen (20th century)