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Kharat, Vilas
- Some Characterizations of Upper Semimodular Lattices and Posets
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Authors
R. S Shewale
1,
Vilas Kharat
2
Affiliations
1 Sinhgad College of Engineering, Pune 411 041, IN
2 Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, IN
1 Sinhgad College of Engineering, Pune 411 041, IN
2 Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, IN
Source
The Journal of the Indian Mathematical Society, Vol 82, No 3-4 (2015), Pagination: 189-205Abstract
In this paper, we introduce two new conditions that give a distinctive description of upper semimodularity in finite lattices. Their relations with the existing conditions due to Mac Lane are established. Also, all these conditions for lattices are generalized for posets and relations amongst them are studied. We also give a forbidden structure as a characterization for finite upper semimodular posets. Several counterexamples are constructed.Keywords
Semimodular Lattice, Poset, Mac Lane Conditions, M-Symmetry.
- On the Structure of Pronormal Subgroups of Dihedral Groups
Abstract Views :167 |
PDF Views:0
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.