论文信息 - Finite core- pp -groups

Finite core- pp -groups

Forna positive integer, a groupGis calledcore-nifH/H Ghas order at mostnfor every subgroupHofG(whereH Gis the normal core ofH, the largest normal subgroup ofGcontained inH). It is proved that a finite core-pp-groupGhas a normal abelian subgroup whose index inGis at mostp 2ifpâ� 2, which is the best possible bound, and at most 2 6ifp=2. Â© 1997 Academic Press.

[1] J. Wiegold,et al. Locally graded groups with all subgroups normal-by-finite , 1996 .

[2] J. Wiegold,et al. Some finiteness conditions concerning intersections of conjugates of subgroups , 1995 .

[3] A. Ol'shanskii,et al. Geometry of Defining Relations in Groups , 1991 .

[4] J. D. Gillam. A note on finite metabelian $p$-groups , 1970 .

[5] B. H. Neumann,et al. Groups with all subgroups normal-by-finite , 1995 .

[6] B. A. F. Wehrfritz,et al. Locally finite groups , 1973 .

[7] M. Newman. On a Class of Nilpotent Groups , 1960 .

[8] J. Lennox,et al. Subnormal Subgroups of Groups , 1987 .

[9] B. H. Neumann,et al. Groups with finite classes of conjugate subgroups , 1955 .

[10] J. Wiegold,et al. Locally Finite Groups All of Whose Subgroups are Boundedly Finite over Their Cores , 1997 .