An Application of Maximality to Nilpotent and Finitely Generated L-Subgroups of an L-Group

TL;DR

This paper extends the study of maximal and Frattini L-subgroups in L-groups, focusing on nilpotent cases and finitely generated subgroups, revealing new properties and relations.

Contribution

It introduces finitely generated L-subgroups and explores their relation with maximal conditions, advancing understanding of their structure in L-groups.

Findings

Normality of maximal L-subgroups in nilpotent L-groups

Relation between finitely generated L-subgroups and maximal conditions

Results on Frattini L-subgroups and their properties

Abstract

This paper is a continuation of the study on maximal and Frattini L-subgroups of an L-group. The normality of the maximal L-subgroups of a nilpotent L-group is explored. Then, the concept of finitely generated L-subgroup is introduced and its relation with maximal condition on L-subgroups is established. Thereafter, several results pertaining to the notions of Frattini L-subgroup and finitely generated L-subgroups have been investigated.