No Access

A note on the upper Lie nilpotency index of a group algebra

Meena Sahai

http://orcid.org/0000-0002-2709-9210

Department of Mathematics and Astronomy, University of Lucknow, Lucknow, U.P. 226007, India

E-mail Address: meena_sahai@hotmail.com

Corresponding author.

Search for more papers by this author

and

Bhagwat Sharan

Department of Mathematics and Astronomy, University of Lucknow, Lucknow, U.P. 226007, India

E-mail Address: bhagwat_sharan@hotmail.com

Search for more papers by this author

https://doi.org/10.1142/S1793557120500102Cited by:3 (Source: Crossref)

Abstract

In this paper, we classify the modular group algebra $K G$ of a group $G$ over a field $K$ of characteristic $p > 0$ having upper Lie nilpotency index $t^{L} (K G) = 9 p - 7$ . The group algebra $K G$ with $t^{L} (K G) < 9 p - 7$ has already been described.

Communicated by N. Gilbert

Keywords:

AMSC: 16S34, 17B30

References

1. V. Bovdi, Modular group algebras with almost maximal Lie nilpotency indices II, Sci. Math. Jpn. 65 (2007) 267–271. Google Scholar
2. V. Bovdi, T. Juhasz and E. Spinelli, Modular group algebras with maximal Lie nilpotency indices, Algebr. Represent. Theory 9(3) (2006) 259–266. Crossref, Web of Science, Google Scholar
3. V. Bovdi and J. Kurdics, Lie properties of the group algebras and the nilpotency class of the group of Units, J. Algebra 212(1) (1999) 28–64. Crossref, Web of Science, Google Scholar
4. V. Bovdi and E. Spinelli, Modular group algebras with maximal Lie nilpotency indices, Publ. Math. Debrecen 65(1–2) (2004) 243–252. Crossref, Web of Science, Google Scholar
5. V. Bovdi and J. B. Srivastava, Lie nilpotency indices of modular group algebra, Algebra Colloq. 17(1–2) (2010) 17–26. Link, Web of Science, Google Scholar
6. The GAP Groups, Algorithms and Programming, Version 4.7.8 (2015), http://www.gap-system.org. Google Scholar
7. R. James, Groups of order $p^{6}$ ( $p$ is an odd prime), Math. Comp. 34(150) (1980) 613–637. Web of Science, Google Scholar
8. Z. Qinhai, S. Qiangwei and X. Mingyai, A classification of some regular p-groups and its applications, Sci. China Ser. A Math. 49(3) (2006) 366–386. Crossref, Web of Science, Google Scholar
9. M. Sahai, Group algebras with almost minimal Lie nilpotency index, Publ. Math. Debrecen 87(1–2) (2015) 47–55. Crossref, Web of Science, Google Scholar
10. M. Sahai and B. Sharan, On Lie nilpotent modular group algebras, Comm. Algebra 46(3) (2018) 1199–1206. Crossref, Web of Science, Google Scholar
11. M. Sahai and B. Sharan, Modular group algebras of Lie nilpotency index $8 p - 6$ , Asian- Eur. J. Math. 11 (2018), Article ID: 1850039, 11 pp. Link, Web of Science, Google Scholar
12. A. Shalev, Lie dimension subgroups, Lie nilpotency indices and the exponent of the group of normalized units, J. London Math. Soc. 43 (1991) 23–36. Crossref, Web of Science, Google Scholar
13. A. Shalev, The nilpotency class of the unit group of a modular group algebra III, Arch. Math. 60 (1993) 136–145. Crossref, Web of Science, Google Scholar
14. R. K. Sharma and V. Bist, A note on Lie nilpotent group rings, Bull. Austral. Math. Soc. 45 (1992) 503–506. Crossref, Web of Science, Google Scholar