Conjugate L-subgroups of An L-group and Their Applications to Normality and Normalizer

Abstract

In this paper, the notion of the conjugate of an L-subgroup by an L-point has been introduced. Then, several properties of conjugate L-subgroups have been studied analogous to their group-theoretic counterparts. Also, the notion of conjugacy has been investigated in the context of normality of L-subgroups. Furthermore, some important relationships between conjugate L-subgroups and normalizer have also been established. Finally, the normalizer of an L-subgroup has been defined by using the notion of conjugate L-subgroups.

Keywords:

• L-group
• L-subgroup
• Conjugate L-subgroup
• Normal L-subgroup
• Normalizer of An L-subgroup

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The second author of this paper was supported by the Senior Research Fellowship jointly funded by CSIR and UGC, India during the course of development of this paper.

Notes on contributors

Iffat Jahan

Iffat Jahan did her Ph.D. from Department of Mathematics, University of Delhi, India, in 2014. She is working as a Professor in the Department of Mathematics, Ramjas College, University of Delhi, India. She has authored more than 15 research papers in the area of L-Group Theory. Her areas of interest and research are Group Theory, Ring Theory, Lattice Theory, and Fuzzy Sets.

Ananya Manas

Ananya Manas is a doctoral student at Department of Mathematics, University of Delhi. His areas of research are Group Theory, Lattice Theory, and L-Groups.