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Sonsuz Grupların Çapraz Çarpımı için Tam Yeniden Yazma Sistemi

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 112 - 118, 28.02.2020

Eylem Karpuz , Ayşe Çevik Esra Kırmızı Çetinalp

https://doi.org/10.18185/erzifbed.638139

Abstract

Bu
çalışmada; ilk olarak iki serbest grubun çapraz çarpımının monoid sunuşu için
kelime probleminin çözülebilir olduğu incelenmiştir. Bunun için teorik
bilgisayar biliminde de önemli bir yeri olan yeniden yazma sistemi tekniği
kullanılmıştır. Daha sonra ise rankları 2 olan iki serbest abelyan grubun
çapraz çarpımının sunuşu elde edilmiştir.

Keywords

Yeniden Yazma Sistemi Kelime Problemi Çapraz çarpım

References

  • Abuhlail, J. Y. 2005. “Duality Theorems for Crossed Products over Rings”, Journal of Alg., 288 (1), 212-240.
  • Agore, A. L. ve Militaru, G. 2008. “Crossed Product of Groups, Applications”, Arab. J. Sci. Eng., 33, 1-17.
  • Agore, A. L. ve Fratila, D. 2010. “Crossed Product of Cyclic Groups”, Czechoslov. Math. J., 60(135), 889-901.
  • Book, R. V. 1987. “Thue Systems as Rewriting Systems”, J. Symbolic Computation, 3(1-2), 39-68.
  • Book, R. V. ve Otto, F. (1993). “String Rewriting Systems”, Springer-Verlag, New York.
  • Carbani,G., Guccione, J. A. ve Guccione, J. J. 2010. “Cyclic Homology of Hopf Crossed Products”, Adv. in Math., 223(3), 840-872.
  • Çetinalp, E. K. 2016 “Bazı Grup ve Monoid Yapıları için Karar Verme Problemleri ve Büyüme Serileri”, Yüksek Lisans Tezi, Karamanoğlu Mehmetbey Üniversitesi Fen Bilimleri Enstitüsü, Karaman.
  • Çetinalp, E. K., Karpuz, E. G. , Ateş, F. ve Çevik, A. S. 2016. “Two-Sided Crossed Products of Groups”, Filomat, 30 (4), 1005-1012.
  • Çetinalp, E. K. ve Karpuz, E. G. 2018. “Iterated Crossed Product of Cyclic Groups”, Bulletin of the Iranian Math. Society, 44(6), 1493-1508.
  • Dehn, M. 1911. “Uber unendliche diskontinuerliche Gruppen”, Math. Ann., 69, 116-144.
  • Grundling, H. ve Neeb, K. H. 2014. “Crossed Products of C*-Algebras for Singular Actions”, Journal of Func. Analysis, 266 (8), 5199-5269.
  • Emin, A., Ateş, F., İkikardeş, S. ve Cangül, İ. N. 2013. “A New Monoid Construction under Crossed Products”, Journal of Inequalities and Applications, 244.
  • Karpuz, E. G. ve Çetinalp, E. K. 2016. “Growth Series of Crossed and Two-Sided Crossed Products of Cyclic Groups”, Mathematica Slovaca, 68(3), 537-548.
  • Miller, F. C. (1992). “Decision Problems For Groups-Survey and Reflections in Algorithms and Classification in Combinatorial Group Theory”, MSRI Publications, Springer-Verlag, 23, 1-59.
  • Rudkovskii, M. A. 1997. “Twisted Product of Lie Groups”, Siberian Math. Journal, 38, 1120- 1129.
  • Sims, C. C. (1994). “Computation with Finitely Presented Group”, Cambridge University Press.

Complete Rewriting System for Crossed Product of Infinite Groups

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 112 - 118, 28.02.2020

Eylem Karpuz , Ayşe Çevik Esra Kırmızı Çetinalp

https://doi.org/10.18185/erzifbed.638139

Abstract

In this work, firstly, it is investigated the solvability of the word problem for monoid presentation of crossed

product of two free groups. To do that it is used rewriting system method which has an important role in

theoretical computer science. Then it is obtained a presentation for crossed product of two free abelian groups

of rank 2.

Keywords

Rewriting System Word Problem Crossed Product

References

  • Abuhlail, J. Y. 2005. “Duality Theorems for Crossed Products over Rings”, Journal of Alg., 288 (1), 212-240.
  • Agore, A. L. ve Militaru, G. 2008. “Crossed Product of Groups, Applications”, Arab. J. Sci. Eng., 33, 1-17.
  • Agore, A. L. ve Fratila, D. 2010. “Crossed Product of Cyclic Groups”, Czechoslov. Math. J., 60(135), 889-901.
  • Book, R. V. 1987. “Thue Systems as Rewriting Systems”, J. Symbolic Computation, 3(1-2), 39-68.
  • Book, R. V. ve Otto, F. (1993). “String Rewriting Systems”, Springer-Verlag, New York.
  • Carbani,G., Guccione, J. A. ve Guccione, J. J. 2010. “Cyclic Homology of Hopf Crossed Products”, Adv. in Math., 223(3), 840-872.
  • Çetinalp, E. K. 2016 “Bazı Grup ve Monoid Yapıları için Karar Verme Problemleri ve Büyüme Serileri”, Yüksek Lisans Tezi, Karamanoğlu Mehmetbey Üniversitesi Fen Bilimleri Enstitüsü, Karaman.
  • Çetinalp, E. K., Karpuz, E. G. , Ateş, F. ve Çevik, A. S. 2016. “Two-Sided Crossed Products of Groups”, Filomat, 30 (4), 1005-1012.
  • Çetinalp, E. K. ve Karpuz, E. G. 2018. “Iterated Crossed Product of Cyclic Groups”, Bulletin of the Iranian Math. Society, 44(6), 1493-1508.
  • Dehn, M. 1911. “Uber unendliche diskontinuerliche Gruppen”, Math. Ann., 69, 116-144.
  • Grundling, H. ve Neeb, K. H. 2014. “Crossed Products of C*-Algebras for Singular Actions”, Journal of Func. Analysis, 266 (8), 5199-5269.
  • Emin, A., Ateş, F., İkikardeş, S. ve Cangül, İ. N. 2013. “A New Monoid Construction under Crossed Products”, Journal of Inequalities and Applications, 244.
  • Karpuz, E. G. ve Çetinalp, E. K. 2016. “Growth Series of Crossed and Two-Sided Crossed Products of Cyclic Groups”, Mathematica Slovaca, 68(3), 537-548.
  • Miller, F. C. (1992). “Decision Problems For Groups-Survey and Reflections in Algorithms and Classification in Combinatorial Group Theory”, MSRI Publications, Springer-Verlag, 23, 1-59.
  • Rudkovskii, M. A. 1997. “Twisted Product of Lie Groups”, Siberian Math. Journal, 38, 1120- 1129.
  • Sims, C. C. (1994). “Computation with Finitely Presented Group”, Cambridge University Press.
There are 16 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Eylem Karpuz 0000-0002-7111-3462

Ayşe Çevik This is me 0000-0002-7538-6652

Esra Kırmızı Çetinalp 0000-0002-3754-8622

Publication Date February 28, 2020
Published in Issue Year 2020 Volume: 13 Issue: ÖZEL SAYI I

Cite

APA Karpuz, E., Çevik, A., & Kırmızı Çetinalp, E. (2020). Sonsuz Grupların Çapraz Çarpımı için Tam Yeniden Yazma Sistemi. Erzincan University Journal of Science and Technology, 13(ÖZEL SAYI I), 112-118. https://doi.org/10.18185/erzifbed.638139