Advanced search
Publication Cover
Communications in Algebra Volume 49, 2021 - Issue 9
Submit an article Journal homepage
98
Views
0
CrossRef citations to date
0
Altmetric
Articles

Central units in some integral group rings

Vitor Araujo GarciaDepartamento de Matemática, Universidade de São Paulo, São Paulo, BrazilCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0001-6150-5633View further author information
ORCID Icon &
Raul Antonio FerrazDepartamento de Matemática, Universidade de São Paulo, São Paulo, BrazilView further author information
Pages 4000-4015 | Received 13 Nov 2020, Accepted 24 Mar 2021, Published online: 27 Apr 2021

References

  • Aleev, R. Z. (1994). Higman’s central unit theorem, units of integral group rings and Fibonacci numbers. Int. J. Algebra Comput. 04(03):309–358. DOI: 10.1142/S0218196794000038.
  • Aleev, R. Z., Panina, Z. (2000). The units of cyclic groups of order 7 and 9. Rus. Math. 43:80–83.
  • Aleev, R. Z., Sokolov, V. V. (2009). On central unit groups of integral group rings of alternating groups. Proc. Steklov Inst. Math. 267(S1):S1–S9. DOI: 10.1134/S0081543809070013.
  • Borevich, Z. I., Shafarevich, I. R. (1966). Number Theory, Pure and Applied Mathematics. Cambridge, MA: Academic Press.
  • Cohn, J. A., Livingstone, D. (1965). On the structure of group algebras. Can. J. Math. 17:583–593. DOI: 10.4153/CJM-1965-058-2.
  • Ferraz, R. A. (2002). Subgrupos Livres e Unidades Centrais No Grupo de Unidades de Alguns Anéis de Grupos. São Paulo: Universidade de São Paulo.
  • Ferraz, R. A. (2009). Units of ZCp, Groups, Rings and Group Rings, Contemporary Mathematics, Vol. 499. Providence, RI: American Mathematical Society, pp. 107–119.
  • Ferraz, R. A., Kitani, P. M. (2015). Units of ZCpn. Commun. Algebra 43:4936–4950.
  • Ferraz, R. A., Marcuz, R. (2016). Units of Z(Cp×C2) and Z(Cp×C2×C2). Commun. Algebra 44(2):851–872.
  • Ferraz, R. A., Simón, J. J. (2008). Central units in metacyclic integral group rings. Commun. Algebra 36(10):3708–3722. DOI: 10.1080/00927870802158028.
  • Ferraz, R. A., Simón, J. J. (2016). Central units in ZCp,q. Commun. Algebra 44(5):2264–2275.
  • Hoechsmann, K. (1989). Généralization d’un lemme de Kummer. Can. Math. Bull. 32(4):486–489.
  • Hoechsmann, K., Sehgal, S. K. (1986). Units in regular elementary abelian group rings. Arch. Math. 47(5):413–417. DOI: 10.1007/BF01189981.
  • Jespers, E., Olteanu, G., del Río, Á., Gelder, I. V. (2013). Group rings of finite strongly monomial groups: Central units and primitive idempotents. J. Algebra 387:99–116. DOI: 10.1016/j.jalgebra.2013.04.020.
  • Polcino Milies, C., Sehgal, S. K. (2002). An Introduction to Group Rings. Amsterdam: Kluwer Academic Publishers.
  • Sehgal, S. K. (1993). Units in Integral Group Rings. London: Longman Scientific & Technical.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.