准素子群正规化子有素数幂指数的有限群

Finite Groups with Normalizers of Primary Subgroups Having Prime Power Indices

研究准素子群正规化子有素数幂指数的有限群.证明了:如果一个有限群G的所有准素子群的正规化子有素数幂指数,则对于任意素数p,G的p长≤1.同时也给出了其它相关结果.

In this paper, finite groups in which the index of the normalizer of every primary subgroup is a prime power are studied. Some relevant results are proved that if the index of the normalizer of every primary subgroup of a finite group G is a prime power, then the plength of the group G is at most 1, for every prime p, as well as if G is a {p,q}soluble group and |G:NG(Gp)|=qα (α≥0), then lπ≤1+lq(G).