Have a personal or library account? Click to login
Equivalent Expressions of Direct Sum Decomposition of Groups1 Cover

Equivalent Expressions of Direct Sum Decomposition of Groups1

Formalized Mathematics
Volume 23 (2015): Issue 1 (March 2015)
By: Kazuhisa Nakasho,  Hiroyuki Okazaki,  Hiroshi Yamazaki and  Yasunari Shidama  
Open Access
|Mar 2015

References

  1. [1] Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589–593, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563–567, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213–225, 1992.
    Search in Google Scholar
  4. [4] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.
    Search in Google Scholar
  5. [5] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990.
    Search in Google Scholar
  6. [6] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.
    Search in Google Scholar
  7. [7] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485–492, 1996.
    Search in Google Scholar
  8. [8] Nicolas Bourbaki. Elements of Mathematics. Algebra I. Chapters 1-3. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989.
    Search in Google Scholar
  9. [9] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.
    Search in Google Scholar
  10. [10] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.
    Search in Google Scholar
  11. [11] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357–367, 1990.
    Search in Google Scholar
  12. [12] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.
    Search in Google Scholar
  13. [13] Artur Korniłowicz. The product of the families of the groups. Formalized Mathematics, 7(1):127–134, 1998.
    Search in Google Scholar
  14. [14] Serge Lang. Algebra. Springer, 3rd edition, 2005.
    Search in Google Scholar
  15. [15] Beata Madras. Product of family of universal algebras. Formalized Mathematics, 4(1): 103–108, 1993.
    Search in Google Scholar
  16. [16] Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, and Yasunari Shidama. Definition and properties of direct sum decomposition of groups. Formalized Mathematics, 23 (1):15–27, 2015. doi:10.2478/forma-2015-0002.10.2478/forma-2015-0002
    Search in Google Scholar
  17. [17] Hiroyuki Okazaki, Kenichi Arai, and Yasunari Shidama. Normal subgroup of product of groups. Formalized Mathematics, 19(1):23–26, 2011. doi:10.2478/v10037-011-0004-7.10.2478/v10037-011-0004-7
    Search in Google Scholar
  18. [18] D. Robinson. A Course in the Theory of Groups. Springer New York, 2012.
    Search in Google Scholar
  19. [19] J.J. Rotman. An Introduction to the Theory of Groups. Springer, 1995.10.1007/978-1-4612-4176-8
    Search in Google Scholar
  20. [20] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115–122, 1990.
    Search in Google Scholar
  21. [21] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569–573, 1990.
    Search in Google Scholar
  22. [22] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990.
    Search in Google Scholar
  23. [23] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5): 855–864, 1990.
    Search in Google Scholar
  24. [24] Wojciech A. Trybulec. Classes of conjugation. Normal subgroups. Formalized Mathematics, 1(5):955–962, 1990.
    Search in Google Scholar
  25. [25] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41–47, 1991.
    Search in Google Scholar
  26. [26] Wojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group. Formalized Mathematics, 2(4):573–578, 1991.
    Search in Google Scholar
  27. [27] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.
    Search in Google Scholar
  28. [28] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990.
    Search in Google Scholar
  29. [29] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181–186, 1990.
    Search in Google Scholar
DOI: https://doi.org/10.2478/forma-2015-0006 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Journal RSS Feed
Language: English
Page range: 67 - 73
Submitted on: Feb 26, 2015
|
Published on: Mar 31, 2015
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
20E34,
03B35
Related subjects:
Mathematics,
General mathematics,
Computer sciences,
Computer sciences, other

© 2015 Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Previous articleVolume 23 (2015): Issue 1 (March 2015)