Have a personal or library account? Click to login
A generalized Goursat lemma Cover

References

  1. [AC09] ANDERSON, D. D.-CAMILLO, V.: Subgroups of direct products of groups, ideals and subrings of direct products of rings, and Goursat’s lemma, in: Internat.
  2. Conference on Rings and Things in honor of C. Faith and B. Osofsky (N. V. Dung et al., eds.), Zanesville, OH, USA, 2007, Contemp. Math., Vol. 480, Amer. Math.
  3. Soc., Providence, RI, 2009, pp. 1-12.
  4. [AEM09] ARROYO, C.-EGGLESTON, S.-MACGREGOR, B.: Applications and generalizations of Goursat’s lemma, 2009, http://www.slideshare.net/dadirac/goursats-lemma-presentation-2411944
  5. [Baer40] BAER, R.: Sylow theorems for infinite groups, Duke J. Math. 6 (1940), 518-614.
  6. [CLP93] CARBONI, A.-KELLY, G. M.-PEDIICCHIO, M. C.: Some remarks on Mal’- tsev and Goursat categories, Appl. Categ. Structures 1 (1993), 385-421.10.1007/BF00872942
  7. [Dic69] DICKSON, S. E.: On algebras of finite representation type, Trans. Amer. Math. Soc. 135 (1969), 127-141.10.1090/S0002-9947-1969-0237558-9
  8. [DKU38] DIEMAN, A. P.-KUROSH, A. G.-UZKOV, A. L.: Sylowsche Untergruppen von unendlichen Gruppen, Mat. Sb. 3 (1938), 179-185.
  9. [Dir1837] DIRICHLET, P. G. L.: Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unenlich viele Primzahlen enthält, Abhang. Ak. Wiss.
  10. Berlin 48 (1837), 45-81.
  11. [FL10] FARRILL, J. F.-LACK, S.: For which categories does one have a Goursat lemma?, 2010, http://mathoverflow.net/questions/46700/for-whichcategories-does-one-have-a-goursat-lemma
  12. [Gou89] GOURSAT, É.: Sur les substitutions orthogonales et les divisions régulières de l’espace, Ann. Sci. École Norm. Sup. (3) 6 (1889), 9-102.10.24033/asens.317
  13. [Gre09] GREICIUS, A.: Elliptic curves with surjective adelic Galois representations, arXiv:0901.2513v1, 2009.
  14. [Hall59] HALL, M., JR.: The Theory of Groups. Macmillan, New York, 1959.10.4159/harvard.9780674592711
  15. [Hat61] HATTORI, A.: On 3-dimensional elliptic space forms, Sūgaku 12 (1960/1961), 164-167.
  16. [HZ09] HATTORI, A.-MARTINS, L.-MASSAGO, S.-MIMURA, M.-ZVENGROWSKI, P.: Three-dimensional spherical space forms, in: Group Actions and Homogeneous Spaces (J. Korbaš et al., eds.), Proc. of the Internat. Conf., Bratislava Topology Symposium, Univ. Komenskho, Fakulta Matematiky, Fyziky a Informatiky, Bratislava, 2010, pp. 29-42.
  17. [Lam58] LAMBEK, J.: Goursat’s theorem and the Zassenhaus lemma, Canad. J. Math. 10 (1958), 45-56.10.4153/CJM-1958-005-6
  18. [Lam76] , Lectures on Rings and Modules (2nd ed.). Chelsea Publishing Co., New York, 1976.
  19. [Lan02] LANG, S.: Algebra (3rd ed.), in: Grad. Texts in Math., Vol. 211, Springer-Verlag, New York, 2002.
  20. [Mac71] MACLANE, S.: Categories for the Working Mathematician, in: Grad. Texts in Math., Vol. 5, Springer-Verlag, New York, 1971.
  21. [Neu67] NEUMANN, H.: Varieties of Groups, in: Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 37, Springer-Verlag, New York, 1967.
  22. [Pet09] PETRILLO, J.: Goursat’s other theorem, College Math. J. 40 (2009), 119-124. [Pet11] , 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
  23. [Ram-Val99] RAMAKRISHNAN, D.-VALENZA, R. J.: Fourier Anaalysis on Number Fields, in: Grad. Texts in Math., Vol. 186, Springer-Verlag, New York, 1999.10.1007/978-1-4757-3085-2
  24. [Rib76] RIBET, K. A.: Galois action on division points of abelian varieties with real multiplications, Amer. J. Math. 98 (1976), 751-804.10.2307/2373815
  25. [Rob82] ROBINSON, D.: A Course in the Theory of Groups, in: Grad. Texts in Math., Vol. 80, Springer-Verlag, New York, 1982.
  26. [Rot95] ROTMAN, J.: An Introduction to the Theory of Groups (4th ed.), in: Grad. Texts in Math., Vol. 148, Springer-Verlag, New York, 1995.10.1007/978-1-4612-4176-8
  27. [Sch94] SCHMIDT, R.: Subgroup Lattices of Groups, in: de Gruyter Exp. Math., Vol. 14, Walter de Gruyter & Co., Berlin, 1994.10.1515/9783110868647
  28. [T´oth14] TÓTH, L.: Subgroups of finite Abelian groups having rank two via Goursat’s Lemma, Tatra Mt. Math. Publ. 59 (2014), 93-103. [Use91] USENKO, V. M.: Subgroups of semidirect products, Ukrain.Mat. Zh. 43 (1991), 1048-1055.
DOI: https://doi.org/10.1515/tmmp-2015-0039 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 1 - 19
Submitted on: Nov 2, 2015
Published on: Feb 19, 2016
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2016 Kristine Bauer, Debasis Sen, Peter Zvengrowski, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.