“Sylow's theorems”的概念、定义、习题解题方法及翻译-数学辞典

单词

Sylow's theorems

释义

Sylow's theorems

Three theorems due to the Norwegian mathematician Peter Sylow which provide partial converses to Lagrange's theorem. Let G be a group of order pam, where p is a prime which does not divide m and a is a positive integer. Then:

1ST THEOREM: G has a subgroup of order pa. Any such subgroup is called a Sylow p-subgroup.

2ND THEOREM: Any two Sylow p-subgroups are conjugate in G.

3RD THEOREM: If there are np Sylow p-subgroups in G, then np divides m and p divides np–1.

Sylow's theorems have more significance when G's order is divisible by several primes, but imply nothing useful about groups whose orders are a power of a prime.

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