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Agalave, Manish
- On the Structure of Pronormal Subgroups of Dihedral Groups
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Authors
Affiliations
1 Department of Mathematics, S. P. Pune University, Pune 411007, IN
1 Department of Mathematics, S. P. Pune University, Pune 411007, IN
Source
The Journal of the Indian Mathematical Society, Vol 90, No 3-4 (2023), Pagination: 401–410Abstract
In this paper, we study the structure of the collection of pronormal subgroups of dihedral groups Dn for different values of n. We enumerate the number of pronormal subgroups of Dn when n is some power of 2. Also, the relation of the collection of all pronormal subgroups with normal subgroups and all subgroups of Dn for different values of n are studied.Keywords
Group, Normal Subgroup, Pronormal Subgroup, Maximal Subgroup, Hall Subgroup, Lattice of Subgroups.
References
- G. Birkhoff, Lattice Theory, Amer. Math Soc. Pub XXV. 3rd Ed providence, 1967.
- B. Brewster, A. Martinez-Pastor and M. D. Perez-Ramos, Pronormal Subgroups of Direct product of groups, J. Algebra, 321(2009), 1734–1745.
- S. R. Cavior, The Subgroups of the Dihedral Group, Mathematics Magazine, 48:2(1975), 107–
- S. K. Chebolu, and K. Lockridge, Fuchs’ Problem for Dihedral Groups, J. Pure Appl. Algebra, 221(2017), 971–982.
- K. Conrad Dihedral Groups II, https://kconrad.math.uconn.edu/blurbs/grouptheory/dihedral2.pdf
- H. Darabi, and M. Imanparast, Counting Number of Fuzzy Subgroups of Some of Dihedral Groups, Int. J. Pure and Applied Mathematics, 85(3)(2013), 563–575.
- A. S. Kondrat, N. V. Maslova, and D. O. Revin, On pronormal Subgroups of Finite Simple Groups, Doklady Akademii Nauk, 98(2018), 405–482.
- J. Liu, J. Chang and G. Chen, Finite Groups with Some Pronormal subgroups, J. Algebra Appl, 19(6)2050110(2020), 8 pages.
- A. Mann, A Criterion for Pronormality, J. London Math. Soc., 44(1969), 175–176.
- Palfy, P. P., Groups and Lattices, London. Math. Soc. Lecture Note Ser., 305(2003), 428–454.
- T. A. Peng, Pronormality in Finite Groups, J. London Math. Soc.(2), 3(1971), 301–306.
- J. S. Rose, Finite Soluble Groups with Pronormal System Normalizers, Proc. London Math. Soc.(3), 17(1969), 447–469.
- Schmidt, R., Subgroup Lattices of Groups, de Gruyter Expositions in Mathematics 14 de Gruyter, Berlin, 1994.
- M. Suzuki, Structure of a Group and the Structure of its Lattice of Subgroups Springer Verlag, Berlin, 1956.
- E. P. Vdovin, and D. O. Revin, Pronormality and Strong Pronormality of Subgroups, Algebra Logic, 52(2013), 15–23.