Geodesic
On some subgroup lattices of dihedral, alternating and symmetric groups
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 309-326

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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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Mitkari, Shrawani; Kharat, Vilas; Ballal, Sachin. On some subgroup lattices of dihedral, alternating and symmetric groups. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 309-326. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a9/