Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T23:07:22.441Z Has data issue: false hasContentIssue false
  • English
  • Français

A characterization of finite p-soluble groups of p-length one by commutator identities

Part of: Special aspects of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Rolf Brandl
Rolf Brandl
Affiliation:
Mathematisches Institut, Am Hubland, D-8700 Würzburg, Federal Republic of Germany
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.

A classical result of M. Zorn states that a finite group is nilpotent if and only if it satisfies an Engel condition. If this is the case, it satisfies almost all Engel conditions. We shall give a similar description of the class of p-soluble groups of p-length one by a sequence of commutator identities.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20F12: Commutator calculus 20F45: Engel conditions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 257 - 263
Copyright
Copyright © Australian Mathematical Society 1981

References

Gorenstein, D. (1968), Finite groups (Harper & Row, New York).Google Scholar
Huppert, B. (1967), Endliche Gruppen I (Springer Verlag, Berlin).CrossRefGoogle Scholar
Zorn, M. (1936), ‘Nilpotency of finite groups’, Bull. Amer. Math. Soc. 42, 485.Google Scholar