Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-13T15:53:02.366Z Has data issue: false hasContentIssue false
  • English
  • Français

Nilpotency indices of the radicals of finite p-solvable group algebras, I

Part of: Rings and algebras arising under various constructions Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Yasushi Ninomiya
Yasushi Ninomiya
Affiliation:
Department of Mathematical Sciences Faculty of Science Shinshu University Matsumoto390-8621Japan e-mail: ysninom@gipac.shinshu-u.ac.jp
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 k be a field of characteristic p > 0, G a finite p-solvable group and pm the highest power of p dividing the order of G. We denote by t(G) the nilpotency index of the (Jacobson) radical of the group algebra k[G]. The groups G with t(G) ≥ pm−1 are already classified. The aim of this paper is to classify the p-solvable groups G with pm−2 < t(G) < pm−1 for p odd.

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 16S34: Group rings , Laurent polynomial rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 1 , August 2001 , pp. 117 - 133
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Conway, J., Curtis, R., Norton, S., Parker, R. and Wilson, R., Atlas of finite groups (Clarendon Press, Oxford, Amsterdam, 1985).Google Scholar
[2]Hall, P. and Higman, G., ‘On the p-length of p-solvable groups and reduction theorems for Burnside's problem’, Proc. London Math. Soc. (3) 6 (1956), 1–42.CrossRefGoogle Scholar
[3]Karpilovsky, G., The Jacobson radical of group algebras (North-Holland, Amsterdam, 1987).Google Scholar
[4]Motose, K., ‘On the nilpotency index of the radical of a group algebra, III’, J. London Math. Soc. (2) 25 (1982), 39–42.Google Scholar
[5]Ninomiya, Y., ‘Finite p-groups with cyclic subgroups of index p 2’, Math. J. Okayama Univ. 36 (1994), 1–21.Google Scholar
[6]Ninomiya, Y., ‘Nilpotency indices of the radicals of p-group algebras’, Proc. Edinburgh Math. Soc. 37 (1994). 509–517.Google Scholar
[7]Ninomiya, Y., ‘Nilpotency indices of the radicals of finite p-solvable group algebras, II’, Comm. Algebra to appear.Google Scholar
[8]Ninomiya, Y., ‘Nilpotency indices of the radicals of finte p-solvable group algebra III’, preprint, 1999.Google Scholar
[9]Ninomiya, Y., ‘Nilpotency indices of the radicals of finite p-solvable group algebras, IV’, preprint, 1999.Google Scholar
[10]Shalev, A., ‘Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras’, J. Algebra 129 (1990), 412–438.CrossRefGoogle Scholar