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

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

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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