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In mathematics, a Hall subgroup of a finite group ''G'' is a subgroup whose order is coprime to its index. They were introduced by the group theorist . == Definitions == A Hall divisor of an integer ''n'' is a divisor ''d'' of ''n'' such that ''d'' and ''n''/''d'' are coprime. The easiest way to find the Hall divisors is to write the prime factorization for the number in question and take any product of the multiplicative terms (the full power of any of the prime factors), including 0 of them for a product of 1 or all of them for a product equal to the original number. For example, to find the Hall divisors of 60, show the prime factorization is 22·3·5 and take any product of . Thus, the Hall divisors of 60 are 1, 3, 4, 5, 12, 15, 20, and 60. 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''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hall subgroup」の詳細全文を読む スポンサード リンク
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