Article
| Title: | On classes of groups characterized by classes of lattices (English) |
| Author: | Grulović, Milan |
| Author: | Jovanović, Jelena |
| Author: | Šešelja, Branimir |
| Author: | Tepavčević, Andreja |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 1213-1228 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | Classes of groups are identified and characterized in lattice-theoretic terms, i.e., by common properties of the weak congruence lattices of groups in the class. In particular, the necessary and sufficient condition for a class of groups to be a variety has been given in terms of the lattice of weak congruences of groups. (English) |
| Keyword: | lattice of subgroup |
| Keyword: | lattice of weak congruence |
| Keyword: | special element in lattice |
| Keyword: | class of group |
| MSC: | 08A30 |
| MSC: | 20E15 |
| MSC: | 20F99 |
| DOI: | 10.21136/CMJ.2025.0003-25 |
| . | |
| Date available: | 2025-12-20T07:19:29Z |
| Last updated: | 2025-12-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153238 |
| . | |
| Reference: | [1] Ballester-Bolinches, A., Ezquerro, L. M.: Classes of Finite Groups.Mathematics and Its Applications 584. Springer, Dordrecht (2006). Zbl 1102.20016, MR 2241927, 10.1007/1-4020-4719-3 |
| Reference: | [2] Czédli, G., Erné, M., Šešelja, B., Tepavčević, A.: Characteristic triangles of closure operators with applications in general algebra.Algebra Univers. 62 (2009), 399-418. Zbl 1209.08001, MR 2670173, 10.1007/s00012-010-0059-2 |
| Reference: | [3] Czédli, G., Šešelja, B., Tepavčević, A.: On the semidistributivity of elements in weak congruence lattices of algebras and groups.Algebra Univers. 58 (2008), 349-355. Zbl 1144.08002, MR 2415286, 10.1007/s00012-008-2076-y |
| Reference: | [4] Gong, L., Chen, Q., Li, B.: On cyclic actions of finite groups.Mediterr. J. Math. 21 (2024), Article ID 83, 23 pages. Zbl 1550.20019, MR 4725288, 10.1007/s00009-024-02626-z |
| Reference: | [5] Grätzer, G.: General Lattice Theory.Birkhäuser, Basel (2003). Zbl 1152.06300, MR 2451139, 10.1007/978-3-0348-7633-9 |
| Reference: | [6] Grulović, M., Jovanović, J., Šešelja, B., Tepavčević, A.: Lattice characterization of some classes of groups by series of subgroups.Int. J. Algebra Comput. 33 (2023), 211-235. Zbl 1521.20056, MR 4581207, 10.1142/S0218196723500121 |
| Reference: | [7] M. Hall, Jr.: The Theory of Groups.Dover Books on Mathematics. Dover, New York (2018). Zbl 1381.20002, MR 1635901 |
| Reference: | [8] Jovanović, J., Šešelja, B., Tepavčević, A.: Lattice characterization of finite nilpotent groups.Algebra Univers. 82 (2021), Article ID 40, 14 pages. Zbl 1503.20004, MR 4264084, 10.1007/s00012-021-00716-7 |
| Reference: | [9] Jovanović, J., Šešelja, B., Tepavčević, A.: Lattices with normal elements.Algebra Univers. 83 (2022), Article ID 2, 28 pages. Zbl 1515.20110, MR 4346486, 10.1007/s00012-021-00759-w |
| Reference: | [10] Jovanović, J., Šešelja, B., Tepavčević, A.: Nilpotent groups in lattice framework.Algebra Univers. 85 (2024), Article ID 40, 9 pages. Zbl 1550.20052, MR 4800674, 10.1007/s00012-024-00873-5 |
| Reference: | [11] Obraztsov, N. V.: Simple torsion-free groups in which the intersection of any two non-trivial subgroups is non-trivial.J. Algebra 199 (1998), 337-343. Zbl 0898.20017, MR 1489368, 10.1006/jabr.1997.7185 |
| Reference: | [12] Ol'shanskii, A. Y.: An infinite group with subgroups of prime orders.Izv. Akad. Nauk SSSR, Ser. Mat. 44 (1980), 309-321 Russian. Zbl 0475.20025, MR 0571100, 10.1070/IM1981v016n02ABEH001307 |
| Reference: | [13] Ol'shanskii, A. Y.: Geometry of Defining Relations in Groups.Mathematics and Its Applications. Soviet Series 70. Kluwer Academic, Dordrecht (1991). Zbl 0732.20019, MR 1191619, 10.1007/978-94-011-3618-1 |
| Reference: | [14] Pálfy, P. P.: Groups and lattices.Groups St. Andrews 2001 in Oxford. Vol. II London Mathematical Society Lecture Note Series 305. Cambridge University Press, Cambridge (2003), 428-454. Zbl 1085.20508, MR 2051548, 10.1017/CBO9780511542787.014 |
| Reference: | [15] Robinson, D. J. S.: Finiteness Conditions and Generalized Soluble Groups. Part I.Ergebnisse der Mathematik und ihrer Grenzgebiete 62. Springer, Berlin (1972). Zbl 0243.20032, MR 0332989 |
| Reference: | [16] Robinson, D. J. S.: A Course in the Theory of Groups.Graduate Texts in Mathematics 80. Springer, New York (1996). Zbl 0836.20001, MR 1357169, 10.1007/978-1-4419-8594-1 |
| Reference: | [17] Schmidt, R.: Subgroup Lattices of Groups.De Gruyter Expositions in Mathematics 14. Walter de Gruyter, Berlin (1994). Zbl 0843.20003, MR 1292462, 10.1515/9783110868647 |
| Reference: | [18] Šešelja, B., Tepavčević, A.: On CEP and semimodularity in the lattice of weak congruences.Zb. Rad., Prir.-Mat. Fak., Univ. Novom Sadu, Ser. Mat. 22 (1992), 95-106. Zbl 0804.08001, MR 1295228 |
| Reference: | [19] Šešelja, B., Tepavčević, A.: Weak Congruences in Universal Algebra.Institute of Mathematics, Novi Sad (2001). Zbl 1083.08500, MR 1878678 |
| Reference: | [20] Suzuki, M.: Structure of a Group and the Structure of its Lattice of Subgroups.Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge 10. Springer, Berlin (1956). Zbl 0070.25406, MR 0083487, 10.1007/978-3-642-52758-6 |
| Reference: | [21] Traustason, G.: CIP-groups.Arch. Math. 65 (1995), 97-102. Zbl 0829.20041, MR 1338238, 10.1007/BF01270684 |
| Reference: | [22] Vojvodić, G., Šešelja, B.: A note on the modularity of the lattice of weak congruences of a finite group.Contributions to General Algebra 5 Hölder-Pichler-Tempsky, Vienna (1987), 415-419. Zbl 0639.08003, MR 0930939 |
| Reference: | [23] Vojvodić, G., Šešelja, B.: On the lattice of weak congruence relations.Algebra Univers. 25 (1988), 121-130. Zbl 0657.08002, MR 0950740, 10.1007/BF01229965 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
