Conjugate L-Subgroups of an L-group and their Applications to Normality and Normalizer

TL;DR

This paper introduces the concept of conjugates of L-subgroups within L-groups, explores their properties, and investigates their role in normality and normalizers, extending classical group theory concepts to L-group structures.

Contribution

It defines conjugate L-subgroups, studies their properties, and connects conjugacy with normality and normalizers in L-groups, providing new insights into their structure.

Findings

Properties of conjugate L-subgroups established

Relationships between conjugates and normalizers analyzed

Normalizers of L-subgroups defined using conjugates

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 of an L-group has been defined by using the notion of conjugate L-subgroups.