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Subgroups of 3-Factor Direct Products Cover
Open Access
|Aug 2019

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, Alodules and Representations. In: Contemp. Math. Vol. 480, Amer. Math. Soc., Providence, RI, 2009, pp 1–12; http://dx.doi.org/10.1090/conm/480/09364, doi:10.1090/conm/480/09364.10.1090/conm/480/09364,doi:10.1090/conm/480/09364
  2. [2] BAUER, K.—SEN, D. —ZVENGROWSKI, P.: A generalized Goursat lemma, Tatra Mt. Math. Publ. textbf64 (2015) 1–19; doi: 10.1515/tmmp-2015-0039.10.1515/tmmp-2015-0039
  3. [3] BRIDSON, M. R.—HOWIE, J.—MILLER, C. F. III,—SHORT, H.: On the finite presentation of subdirect products and the nature of residually free groups, Amer. J. Math. 135 (2013), no. 4, 891–933; http://dx.doi.org/10.1353/ajm.2013.0036, doi:10.1353/ajm.2013.0036.10.1353/ajm.2013.0036,doi:10.1353/ajm.2013.0036
  4. [4] BRIDSON, M. R.—MILLER, C. F. III.: Structure and finiteness properties of subdirect products of groups. Proc. Lond. Math. Soc. 98 (2009) no. 3, 631–651; http://dx.doi.org/10.1112/plms/pdn039, doi:10.1112/plms/pdn039.10.1112/plms/pdn039,doi:10.1112/plms/pdn039
  5. [5] BUTLER, L. M.: Subgroup lattices and symmetric functions. Mem. Amer. Math. Soc. 112 (1994), no. 539, pp. vi–160; http://dx.doi.org/10.1090/memo/0539, doi:10.1090/memo/0539.10.1090/memo/0539,doi:10.1090/memo/0539
  6. [6] THE GAP GROUP: GAP - Groups, Algorithms, and Programming, Version 4.8.3, 2016; http://www.gap-system.org.
  7. [7] GEKAS, S.: Deciphering subgroups of direct products-, ArXiv e-prints, Septembr 2015. arXiv: 1509.03245.
  8. [8] GOURSAT, E.: Sur les substitutions orthogonales et les divisions réguliѐres de l’espace. Ann. Sci. École Norm. Sup. (3), (1889) 9–102; http://www.numdam.org/item?id=ASEHS_1889_3_6__9_0.10.24033/asens.317
  9. [9] HALL, M. JR.: The theory of groups. Chelsea Publishing Co., New York, 1976. (Reprinting of the 1968 edition)
  10. [10] HAMPEJS, M.—TÓTH, L.: On the subgroups of finite abelian groups of rank three. Ann. Univ. Sci. Budapest. Sect. Comput. 39 (2013), 111–124.
  11. [11] LANG, S.: Algebra (3rd ed.) In: Graduate Texts in Mathematics Vol. 211, Springer-Verlag, New York, 2002. http://dx.doi.org/10.1007/978-l-4613-0041-0, doi: 10.1007/978-1-4613-0041-0.10.1007/978-l-4613-0041-0,doi:10.1007/978-1-4613-0041-0
  12. [12] MILLER, M. D.: On the lattice of normal subgroups of a direct product, Pacific J. Math. 60 (1975) no. 2, 153–158.10.2140/pjm.1975.60.153
  13. [13] PETRILLO, J.: Counting subgroups in a direct product of finite cyclic groups. College Math. J. textbf42 (2011), no. 3, 215–222. http://dx.doi.org/10,4169/college.math.j.42.3.215, doi:10.4169/college.math.j.42.3.215.10.4169/college.math.j.42.3.215
  14. [14] REMAK, R.: Über Untergruppen direkter Produkte von drei Faktoren. J. Reine Angew. Math. 166 (1932), 65–100. http://dx.doi.org/10.1515/crll.1932.166.65, doi:10.1515/crll.1932.166.65.10.1515/crll.1932.166.65,doi:10.1515/crll.1932.166.65
  15. [15] TÓTH, L.: Subgroups of finite abelian groups having rank two via Goursat’s lemma. Tatra Mt. Math. Publ. 59 (2014), 93–103; doi: 10.2478/tmmp-2014-0021.10.2478/tmmp-2014-0021
  16. [16] 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), no. 4, 373–386.
DOI: https://doi.org/10.2478/tmmp-2019-0003 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 19 - 38
Submitted on: Jul 25, 2018
Published on: Aug 15, 2019
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2019 Daniel Neuen, Pascal Schweitzer, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.