关于可解群p—块的几个结果

主要结果是如下定理:设G是有限可解群使得G/F(G)是奇阶A-群,又设p是一个素数且G不含截断q~(pn):(Z_m:Z_p)。其中q~(pn):(Z_m:Z_n))是初等交换q-群q~(pn)被Z_m:Z_p的扩张,而m=(q~(pn)-1)/(q~n-1)。则G有亏数零p-块的充要条件是O_p(G)=1。

Some Results on p-blocks of Solvable Groups

The main result of this note is the followingTheorem Let G be a finite solvable group such that G/F(G) is an A-groups of odd order.Let p be a prime number.Suppose G contains no sections isonaorphic to the extension qPn: (Zm,Zp) of an elementary abelian q-group of order qpn by the group Zm:Zp for any prime number q and any integer n with m= (qpn-1)/(qn-1). Then G has a p-block of defect zero if and only if Op (G) =1.