Conjugate $L$ -Subgroups of An $L$ -Group and Their Applications to Normality and Normalizer

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.