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
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