中心商同构于 p6阶第十九家族的一类 LA-群

摘要

Based on the complete isomorphism classification theory of Rodney James's groups of order p6 ,we continue to study the LA‐group .By using the extension theory of group and the theory of free group , we get a new series of finite p‐groups with central non‐cyclic and quotients being isomorphic to the group of Φ19 (16 ) .Eventually we prove that the groups are new LA‐groups by the characteristic of their automorphisms .%基于Rodney James的 p6阶群的完全同构分类理论，继续LA‐群的研究工作。利用群的扩张理论与自由群理论，得到一类中心非循环且中心商同构与Φ19（16）的有限 p‐群，最后运用自同构的性质证明了此类群是LA‐群。