关于弱半根子群

On Weak Semi-Radicable Subgroups

证明了:①如果局部有限群G的每一个子群H是弱半根群且对任意p∈π(H)满足H≠Hp,那么G是局部幂零群而且每一个Sylow p-子群是有限群．②令G是一个p-群且exp(G)<∞,如果|G:Gp|=∞,但是G 的所有真子群是弱半根群,那么对任意xGp∈G／Gp,其中xGp不属于G／Cp的中心,有G=<z>GGp．

For every subgroup H of a locally finite group G, if H is a weakly semi-radicable group and H≠H^p for every P∈π（H）, then G is a locally nilpotent group and every Sylow p -subgroup of G is finite. Let G be a p -group and expG〈∞,if │G：G^p│=∞ ,but all of proper subgroups of G are weak semi-radicable.Then for every xG^p∈G/G^p,xG^p is not in G/G^p,then G=〈x〉^G G^p.is obtained