一类阶为2·11·p^n的群的构造

The Structures of Groups of Order 2·11·p^n

利用可解群的性质,通过群的扩张理论,给出了Sylowp-子群为循环群时2.11.pn(p≠3奇素数)阶群的构造:①当p≠5,7时,若p≡1(mod 11),有6型;若p 1(mod 11),有4型;②当p=5时有6型;③当p=7时有4型.

In this paper, by using the properties of the solvable group and the extension theory, we prove the structures of groups of 2·11·p^n（p≠3 odd）with Sylow p-subgroups are cyclic groups： ① p≠5, 7：6 types,p≡1（mod 11）; 4 types,p≠1（mod 11）; ② 6 types,p=5;③ 4 types,p=7.