Generalized Normal Subgroups

Abstract

In this paper, we generalize the concept of normal subgroups to N_c-normal subgroups with respect to the variety of all nilpotent groups of class at most c, (c  ≥ 1). We state some properties of Nc-normal subgroups. Also we determine N₂-normal subgroups and N₃-normal subgroups of Q_4n, D_2n, SD_2ⁿ and N_c-normal subgroups of SL(2,F).

Key words and phrases. N_c-normal subgroups, variety of all nilpotent groups, upper central series of a group.

2010 Mathematics Subject Classification. 16U70, 20D15, 20D06