Article in press
Authors:
Shrawani Pravin Mitkari
Department of Mathematics Savitribai Phule Pune University
email: shrawaniin@gmail.com
Vilas Kharat
Department of Mathematics
S.P. Pune University, Pune 411007 India
email: vilaskharat@unipune.ac.in
Title:
Structures of Hall Subgroups of Finite Metacyclic and Nilpotent Groups
PDFSource:
Discussiones Mathematicae - General Algebra and Applications
Received: 2023-08-03 , Revised: 2024-02-23 , Accepted: 2024-02-23 , Available online: 2025-02-18 , https://doi.org/10.7151/dmgaa.1471
Abstract:
In this paper, the structures of Hall subgroups of finite metacyclic
and nilpotent groups are studied. It is proved that the collection of
all Hall subgroups of a metacyclic group is a lattice and a group G
is nilpotent if and only if its collection of Hall subgroups forms a
distributive lattice. Also, lower semimodularity and complementation
are studied in a collection of Hall subgroups of Dn for different values
of n.
Keywords:
group,, Hall subgroup, lattice of subgroups, lower semimodular lattice, metacyclic group, nilpotent group
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