Abnormal and Contranormal L-Subgroups of an L-group

TL;DR

This paper introduces and studies abnormal and contranormal L-subgroups in L-groups, exploring their properties and relationships with other subgroup concepts, extending classical group theory ideas to the L-group context.

Contribution

It defines abnormal and contranormal L-subgroups and investigates their properties and relations within L-groups, extending subgroup theory concepts.

Findings

Properties of abnormal and contranormal L-subgroups established

Relations with normality, maximality, and normalizers analyzed

Analogies with classical group theory demonstrated

Abstract

In this paper, the concepts of abnormal and contranormal L-subgroups of an L-group have been introduced using the notion of the conjugate. Then, the properties of abnormal and contranormal L-subgroups have been studied analogous to their group-theoretic counterparts. Thereafter, several relations of abnormality and contranormality have been investigated in context of normality, maximality, normalizer and normal closure of L-subgroups of an L-group.