一类含p³阶正规子群的奇数阶群

An Odd-Order Group with a Regular Subgroup of Order p³

摘要: 通过研究p³阶群的自同构群的阶从而达到研究奇数阶有限群G含有一个p³阶正规子群N (其中p是G的最小素因子)时所具有的性质，但此时由于群G阶的不确定性故其结构较难得出，故进一步考虑加上条件${\left|G\right|}_p=p^3$ 并如愿得出了G的结构。

Abstract: We mainly study the properties of odd-order finite group G when it contains a p³ order normal subgroup N (where p is the minimum prime factor of G) by studying the automorphism group of the p³ order group, but at this time, due to the order of group G is uncertain, its structure is difficult to find, Therefore, further consideration is given to the addition of the condition ${\left|G\right|}_p=p^3$ and the structure of G is obtained.