Affiliations: [a] Department of Mathematics, Ramjas College, University of Delhi, Delhi, India
| [b] Department of Mathematics, University of Delhi, Delhi, India
Correspondence:
[*]
Corresponding author. I. Jahan, Department of Mathematics, Ramjas College, University of Delhi, Delhi 110007,
India. E-mail: [email protected].
Abstract: In this paper, the concept of a maximal L-subgroup of an L-group has been defined in the spirit of classical group theory. Then, a level subset characterization has been established for the same. Then, this notion of maximal L-subgroups has been used to define Frattini L-subgroup. Further, the concept of non-generators of an L-group has been developed and its relation with the Frattini L-subgroup of an L-group has been established like their classical counterparts. Moreover, several properties pertaining to the concepts of maximal L-subgroups and Frattini L-subgroup have also been investigated. These two notions have been illustrated through several examples.
Keywords: L-algebra, L-subgroup, generated L-subgroup, normal L-subgroup, maximal L-subgroup, Frattini L-subgroup, non-generators of an L-group
