Pronormal L-subgroups of an L-group

TL;DR

This paper introduces the concept of pronormal L-subgroups within L-groups, exploring their properties, relations to normalizers, and their role in the structure of L-groups.

Contribution

It defines pronormal L-subgroups using conjugate L-subgroups and investigates their properties and relationships with normality, subnormality, and maximal L-subgroups.

Findings

Pronormal L-subgroups are characterized in relation to normality and subnormality.

The paper establishes properties connecting pronormality with normalizers.

Relations between pronormal L-subgroups and maximal L-subgroups are analyzed.

Abstract

In this paper, the notion of pronormal L-subgroups of an L-group has been introduced by using the concept of conjugate L-subgroup. The notion of pronormal L-subgroups has been investigated in context of normality and subnormality of L-subgroups and several related properties have been established. Moreover, the relation of pronormality with normalizers and maximal L-subgroups has been explored.