Hostname: page-component-669899f699-qzcqf Total loading time: 0 Render date: 2025-04-26T16:05:37.927Z Has data issue: false hasContentIssue false
  • English
  • Français

Carter subgroups in the group of units of an associative algebra

Published online by Cambridge University Press:  17 April 2009

Thorsten Bauer  and
Salvatore Siciliano
Thorsten Bauer
Affiliation:
Schuetzenwall 43, D–24114 Kiel, Germany, e-mail: [email protected]
Salvatore Siciliano
Affiliation:
Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce, Via Provinciale Lecce-Arnesano, 73100-Lecce, Italy, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

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.

In this paper we examine some properties of the Carter subgroups in the group of units of certain associative algebras. A description of the Carter subgroups in the case of a solvable associative algebra is obtained. Moreover, given an associative algebra A, we study relationships between the Cartan subalgebras of the Lie algebra associated with A and the Carter subgroups of the group of units of A.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 471 - 478
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Carter, R., ‘On a class of finite soluble groups’, Proc. London Math. Soc. 9 (1959), 623–640.CrossRefGoogle Scholar
[2]Volta, F. Dalla, Lucchini, A. and Tamburini, M.C., ‘On the conjugacy problem for Carter subgroups’, Comm. Algebra 26 (1998), 395–401.CrossRefGoogle Scholar
[3]Di Martino, L., Tamburini, M.C. and Zalesskiĭ, A.E., ‘Carter subgroups in classical groups’, J. London Math. Soc. 55 (1997), 264–276.CrossRefGoogle Scholar
[4]Jacobson, N., Lie algebras (Wiley Interscience, New York, 1962).Google Scholar
[5]Jennings, S.A., ‘Central chains of ideals in an associative ring’, Duke Math. J. 9 (1942), 341–355.CrossRefGoogle Scholar
[6]Hallahan, C.H. and Overbeck, J., ‘Cartan subalgebras of meta-nilpotent Lie algebras’, Math. Z. 116 (1970), 215–217.CrossRefGoogle Scholar
[7]Pierce, R.S., Associative algebras (Springer-Verlag, New York, 1982).CrossRefGoogle Scholar
[8]Robinson, D.J.S., A course in the theory of groups (Springer-Verlag, New York, 1982).CrossRefGoogle Scholar
[9]Siciliano, S., ‘Cartan subalgebras in Lie algebras of associative algebras’, (Preprint of the University of Lecce).Google Scholar
[10]Stitzinger, E., ‘Theorems on Cartan subalgebras like some on Carter subgroups’, Trans. Amer. Math. Soc. 159 (1971), 307–315.CrossRefGoogle Scholar
[11]Tamburini, M.C. and Vdovin, E.P., ‘Carter subgroups in finite groups’, J. Algebra 255 (2002), 148–163.CrossRefGoogle Scholar