144
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Nilpotent Lie algebras of breadth type (0, 3)

ORCID Icon, &
Pages 3792-3809 | Received 14 Dec 2022, Accepted 26 Feb 2023, Published online: 21 Mar 2023

References

  • Adams, J. F., Lax, P. D., Phillips, R. S. (1965). On matrices whose real linear combinations are non-singular. Proc. Amer. Math. Soc. 16:318–322. DOI: 10.2307/2033871.
  • Au-yeung, Y. (1971). On matrices whose nontrivial real linear combinations are nonsingular. Proc. Amer. Math. Soc. 29:17–22. DOI: 10.2307/2037666.
  • Barnea, Y., Isaacs, I. M. (2003). Lie algebras with few centralizer dimensions. J. Algebra 259(1):284–299. DOI: 10.1016/S0021-8693(02)00558-6.
  • Camina, A. R., Camina, R. D. (2011). The influence of conjugacy class sizes on the structure of finite groups: a survey. Asian-Eur. J. Math. 4(4):559–588.
  • Cossey, J., Hawkes, T. (2000). Sets of p-powers as conjugacy class sizes. Proc. Amer. Math. Soc. 128(1):49–51.
  • de Graaf, W. A. (2007). Classification of 6-dimensional nilpotent lie algebras over fields of characteristic not 2.J. Algebra 309(2):640–653. DOI: 10.1016/j.jalgebra.2006.08.006.
  • Dolfi, S., Jabara, E. (2009). The structure of finite groups of conjugate rank 2. Bull. Lond. Math. Soc. 41(5):916–926.
  • Dolfi, S. (1995). Arithmetical conditions on the length of the conjugacy classes of a finite group. J. Algebra 174(3):753–771. DOI: 10.1006/jabr.1995.1151.
  • Hall, P. (1940). The classification of prime-power groups. J. Reine Angew. Math. 182:130–141. DOI: 10.1515/crll.1940.182.130.
  • Hurwitz, A. (1922). Über die Komposition der quadratischen Formen. Math. Ann. 88(1–2):1–25.
  • Ishikawa, K. (1999). Finite p-groups up to isoclinism, which have only two conjugacy lengths. J. Algebra220(1):333–345. DOI: 10.1006/jabr.1999.7907.
  • Ishikawa, K. (2002). On finite p-groups which have only two conjugacy lengths. Israel J. Math. 129:119–123. DOI: 10.1007/BF02773158.
  • Ito, N. (1953). On finite groups with given conjugate types. I. Nagoya Math. J. 6:17–28. DOI: 10.1017/S0027763000016937.
  • Ito, N. (1970). On finite groups with given conjugate types. II. Osaka Math. J. 7:231–251.
  • Ito, N. (1970). On finite groups with given conjugate types. III. Math. Z. 117:267–271. DOI: 10.1007/BF01109847.
  • Johari, P., Farangis, N., Parvizi, M. (2021). Nilpotent lie algebras of class 4 with the derived subalgebra of dimension 3. Commun. Algebra 49(2):521–532. DOI: 10.1080/00927872.2020.1803895.
  • Kantor, W. M. (1994). Projective planes of order q whose collineation groups have order q2. J. Algebraic Combin. 3(4):405–425.
  • Khukhro, E. I. (1998). p -automorphisms of Finite p-groups, volume 246 of London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press.
  • Khuhirun, B., Misra, K. C., Stitzinger, E. (2015). On nilpotent Lie algebras of small breadth. J. Algebra 444:328–338.
  • Moneyhun, K. (1994). Isoclinisms in Lie algebras. Algebras Groups Geom. 11(1):9–22.
  • Naik, T. K., Kitture, R. D., Yadav, M. K. (2020). Finite p-groups of nilpotency class 3 with two conjugacy class sizes. Israel J. Math. 236(2):899–930.
  • Naik, T. K., Yadav, M. K. (2018). Finite p-groups of conjugate type {1,p3}. J. Group Theory 21(1):65–82.
  • Parmeggiani, G., Stellmacher, B. (1999). p-groups of small breadth. J. Algebra 213(1):52–68.
  • Radon, J. (1922). Lineare Scharen orthogonaler Matrizen. Abh. Math. Sem. Univ. Hamburg 1(1):1–14.
  • Remm, E. (2017). Breadth and characteristic sequence of nilpotent Lie algebras. Commun. Algebra 45(7):2956–2966.
  • Seeley, C. (1993). 7-dimensional nilpotent Lie algebras. Trans. Amer. Math. Soc. 335(2):479–496.
  • Sheikh-Mohseni, S., Saeedi, F. (2018). Camina Lie algebras. Asian-Eur. J. Math. 11(5):1850063, 11.
  • Sriwongsa, S., Wiboonton, K., Khuhirun, B. (2021). Characterization of nilpotent Lie algebras of breadth 3 over finite fields of odd characteristic. J. Algebra 586:935–972.
  • Wilkens, B. (2007). 2-groups of breadth 3. J. Algebra 318(1):202–224.

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:

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:

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.