Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T06:38:36.409Z Has data issue: false hasContentIssue false
  • English
  • Français

Group Algebras with Minimal Strong Lie Derived Length

Published online by Cambridge University Press:  20 November 2018

Ernesto Spinelli
Ernesto Spinelli*
Affiliation:
Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce, 73100-Lecce, Italy e-mail: ernesto.spinelli@unile.it
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let $KG$ be a non-commutative strongly Lie solvable group algebra of a group $G$ over a field $K$ of positive characteristic $p$. In this note we state necessary and sufficient conditions so that the strong Lie derived length of $KG$ assumes its minimal value, namely $\left\lceil {{\log }_{2}}(p\,+\,1) \right\rceil$.

Keywords

16S3417B30group algebrasstrong Lie derived length
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 2 , 01 June 2008 , pp. 291 - 297
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Catino, F. and E. Spinelli, A note on strong Lie derived length of group algebras. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 10(2007), no. 1, 83–86.Google Scholar
[2] Jennings, S. A., The structure of the group ring of a p-group over a modular field. Trans. Amer. Math. Soc. 50(1941), 175–185.Google Scholar
[3] Levin, F. and Rosenberger, G., Lie metabelian group rings. In: Group and Semigroup Rings. North-Holland Math. Stud. 126, North-Holland, Amsterdam, 1986, pp. 153–161.Google Scholar
[4] Passi, I. B. S., Group rings and their augmentation ideals. Lectures Notes in Mathematics 715, Springer-Verlag, Berlin, 1979.Google Scholar
[5] Passi, I. B. S., Passman, D. S., and Sehgal, S. K., Lie solvable group rings. Canad. J. Math. 25(1973), 748–757.Google Scholar
[6] Rossmanith, R., Lie centre-by-metabelian group algebras in even characteristic. I. Israel J. Math. 115(2000), 51–75.Google Scholar
[7] Sahai, M., Lie solvable group algebras of derived length three. Publ. Mat. 39(1995), no. 2, 233–240.Google Scholar
[8] Sehgal, S. K., Topics in group rings. Monographs and Textbooks in Pure and Applied Math. 50. Marcel Dekker, New York, 1978.Google Scholar
[9] Shalev, A., Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras. J. Algebra 129(1990), 412–438.Google Scholar
[10] Shalev, A., The derived length of Lie soluble group rings. I. J. Pure Appl. Algebra 78(1992), no. 3, 291–300.Google Scholar
[11] Shalev, A. The derived length of Lie soluble group rings. II. J. LondonMath. Soc. 49(1994), no. 1, 93–99.Google Scholar