p^mq^n阶(1≤m,n≤3,p,q为素数)群正规的sylow子群的存在性

The existence of the normal sylow subgroups in p^mq^n order(1≤m,n≤3,p,q is a prime number) groups

目的证明满足一定条件的某阶群为正规sylow子群。方法在掌握群的基本概念的基础上,利用正规子群,sylow子群及正规的sylow子群之间的相互关系,根据sylow子群的定理结合sy-low子群的基本要求,予以解决。结果总结出解决正规sylow群的方法与技巧。结论当p,q为素数,1≤m,n≤2时,pmqn阶群有正规sylow子群。

Aim To prove that a certain order group which meets certain criteria is normal sylow subgroup. Methods Based on basic concept of group, normal subgroup, sylow subgroup and the relationships between normal sylow subgroup are used to prove the proposition according to the sylow subgroup＇s theorem and the essential requirements of sylow subgroup. Results Methods and skills of resolving normal sylow group are summarized. Conclusion When p and q are prime numbers, 1 ≤ m, n ≤ 2, pmqnorder group has normal sylow subgroup.