arXiv subjects

Ananya Manas

Publications and source records attributed to Ananya Manas.

5 recordsLinked to original sources

arXiv2025

Abnormal and Contranormal L-Subgroups of an L-group

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.

math.GR↗

arXiv2025

Pronormal L-subgroups of an L-group

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.

math.GR↗

arXiv2025

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 of an L-group has been defined by using the notion of conjugate L-subgroups.

math.GR↗

arXiv2025

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

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.

math.GR↗

arXiv2020

Maximal and Frattini L-Subgroups of an L-Group

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-subgroups. 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.

math.GR↗