Have a personal or library account? Click to login
Subgroups of Finite Abelian Groups Having Rank Two via Goursat’s Lemma Cover

Subgroups of Finite Abelian Groups Having Rank Two via Goursat’s Lemma

By: László Tóth  
Open Access
|Mar 2015

References

  1. [1] ANDERSON, D. D.-CAMILLO, V.: Subgroups of direct products of groups, ideals and subrings of direct products of rings, and Goursat’s lemma, in: Rings, Modules and Representations. Internat. Conf. on Rings and Things, Zanesville, OH, USA, 2007, Contemp. Math., Vol. 480, Amer. Math. Soc., Providence, RI, 2009, pp. 1-12.10.1090/conm/480/09364
  2. [2] BAUER, K.-SEN, D.-ZVENGROWSKI, P.: A generalized Goursat lemma, Preprint, 2011, arXiv: 11009.0024 [math.GR].
  3. [3] CALHOUN, W. C.: Counting the subgroups of some finite groups, Amer. Math. Monthly 94 (1987), 54-59.10.1080/00029890.1987.12000593
  4. [4] CĂLUGĂREANU, G.: The total number of subgroups of a finite abelian group, Sci. Math. Jpn. 60 (2004), 157-167.
  5. [5] CRAWFORD, R. R.-WALLACE, K. D.: On the number of subgroups of index two- -An application of Goursat’s theorem for groups, Math. Mag. 48 (1975), 172-174.
  6. [6] GOURSAT, É.: Sur les substitutions orthogonales et les divisions régulières de l’espace, Ann. Sci. Ècole Norm. Sup. (3) 6 (1889), 9-102.10.24033/asens.317
  7. [7] HAMPEJS, M.-HOLIGHAUS, N.-TÓTH, L.-WIESMEYR, C.: Representing and counting the subgroups of the group Zm × Zn, Journal of Numbers, Vol. 2014, Article ID 491428.10.1155/2014/491428
  8. [8] HAMPEJS, M.-TÓTH, L.: On the subgroups of finite abelian groups of rank three, Ann. Univ. Sci. Budapest. Eötvös Sect. Comput. 39 (2013), 111-124.
  9. [9] LAMBEK, J.: Goursat’s theorem and the Zassenhaus lemma, Canad. J. Math. 10 (1958), 45-56.10.4153/CJM-1958-005-6
  10. [10] MACHÌ, A.: Groups. An Introduction to Ideas and Methods of the Theory of Groups. Springer, Berlin, 2012.10.1007/978-88-470-2421-2
  11. [11] NOWAK, W. G.-TÓTH, L.: On the average number of subgroups of the group Zm×Zn, Int. J. Number Theory 10 (2014), 363-374.10.1142/S179304211350098X
  12. [12] PETRILLO, J.: Goursat’s other theorem, College Math. J. 40 (2009), 119-124.10.4169/193113409X469569
  13. [13] PETRILLO, J.: Counting subgroups in a direct product of finite cyclic groups, College Math. J. 42 (2011), 215-222.10.4169/college.math.j.42.3.215
  14. [14] ROTMAN, J. J.: An Introduction to the Theory of Groups (4th ed.), in: Grad. Texts in Math., Vol. 148, Springer-Verlag, New York, 1995.
  15. [15] TĂRNĂUCEANU, M.: An arithmetic method of counting the subgroups of a finite Abelian group, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 53(101) (2010), 373-386.
  16. [16] TÓTH, L.: Menon’s identity and arithmetical sums representing functions of several variables, Rend. Sem. Mat. Univ. Politec. Torino 69 (2011), 97-110.
  17. [17] TÓTH, L.: On the number of cyclic subgroups of a finite Abelian group, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(103) (2012), 423-428.
  18. [18] TÓTH, L.: Multiplicative arithmetic functions of several variables: a survey, in: Mathematics Without Boundaries, Surveys in Pure Mathematics (Th. M. Rassias, P. Pardalos, eds.), Springer, New York, 2014, pp. 483-514.10.1007/978-1-4939-1106-6_19
DOI: https://doi.org/10.2478/tmmp-2014-0021 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 93 - 103
Submitted on: Sep 29, 2014
Published on: Mar 11, 2015
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2015 László Tóth, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.