On sylow subgroups of BCI groups
Abstract
The study of BCI-groups was initiated in paper [10] where Xu and Jin proved that every finite group is a 1-BCI-group and a finite group is a 2-BCI-group if and only if it is a FIF-group. Later in [3], Jin and Liu proved that for a prime p, a cyclic group of order 2p is a 3-BCI-group and a cyclic p-group is a (p-l)-BCI-group. In [4], Jin and Liu proved that for a finite 3-BCI-group, its Sylow 2-subgroup is elementary abelian, cyclic or Qs. In this paper, we are continuing the investigation of Sylow p-subgroups of m-BCI-groups. Let G be a finite group and p be an odd prime divisor of |G|. We prove that if G is a 3-BCI-group, then its Sylow p-subgroup is homocyclic. Further, if G is a m-BCI-group such that 2p ≤ m, then its Sylow p-subgroup is either elementary abelian or cyclic.
