DM-GAA

Article in volume

Authors:

V. Kharat

Vilas Kharat

Department of Mathematics
S.P. Pune University, Pune 411007 India

email: vilaskharat@unipune.ac.in

S. Mitkari

Shrawani Pravin Mitkari

Department of Mathematics Savitribai Phule Pune University

email: shrawaniin@gmail.com

S. Ballal

Sachin Ballal

Department of Mathematics
S.P. Pune University, Pune 411007 India

email: sachinballal@uohyd.ac.in

Title:

On some subgroup lattices of dihedral, alternating and symmetric groups

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Source:

Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 309-326

Received: 2021-11-10 , Revised: 2022-05-21 , Accepted: 2022-05-21 , Available online: 2023-01-13 , https://doi.org/10.7151/dmgaa.1425

Abstract:

In this paper, the collections of all pronormal subgroups of $D_n$ and Hall subgroups for groups $A_n$, $S_n$ and $D_n$ are studied. It is proved that the collection of all pronormal subgroups of $D_n$ is a sublattice of $L(D_n)$. It is also proved that the collection of all Hall subgroups of $D_n$, $A_n$ and $S_n$ do not form sublattices of respective $L(D_n)$, $L(A_n)$ and $L(S_n)$.

Keywords:

group, pronormal subgroup, Hall subgroup, lattice of subgroups, strong lattice

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