Infinite locally finite groups with the locally nilpotent non-Dedekind norm of decomposable subgroups

Abstract

The author studies infinite locally finite groups with the locally nilpotent non-Dedekind norm of decomposable subgroups. It is found out that such groups are either p-groups or Frobenius groups, which kernel coincides with the norm of decomposable subgroups. Their structure is described.

Keywords:

• Decomposable group
• locally nilpotent group
• non-Dedekind group
• norm of group
• norm of decomposable subgroups

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D25

Acknowledgment

The author is very grateful to the referee who has read the manuscript carefully and provided a lot of valuable suggestions and useful comments, which improved the paper.