Affiliations: [a] Department of Mathematics, Ramjas College, University of Delhi, Delhi, India
| [b] Department of Mathematics, Yazd University, Iran
| [c] Department of Mathematics, Zakir Husain Delhi College, University of Delhi, Delhi, India
Correspondence:
[*]
Corresponding author. I. Jahan, Department of Mathematics, Ramjas College, University of Delhi, Delhi 110007, India. E-mail: [email protected].
Abstract: In this paper, we study the inter-connections of the notions of commutator L-subgroups, nilpotent L-subgroups, conjugate L-subgroups and normalizer of L-subgroups like their classical counterparts. Throughout the development of this paper, the parent group is an L-group rather than an ordinary group. Our main result in this work is that every nilpotent L-subgroup of an L-group satisfies the normalizer condition.
Keywords: L-algebra, L-subgroup, generated L-subgroup, normal L-subgroup, nilpotent L-subgroup, normal closure, normalizer
