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A particular class of supersoluble groups

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

Published online by Cambridge University Press:  09 April 2009

W. Dirscherl  and
H. Heineken
W. Dirscherl
Affiliation:
Mathematisches Institut der Universität, 97074 Würzburg, Germany
H. Heineken
Affiliation:
Mathematisches Institut der Universität, 97074 Würzburg, Germany
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Abstract

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We consider (finite) groups in which every two-generator subgroup has cyclic commutator subgroup. Among other things, these groups are metabelian modulo their hypercentres, and in the corresponding quotient group all subgroups of the commutator subgroup are normal.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20F12: Commutator calculus 20F16: Solvable groups, supersolvable groups

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 3 , December 1994 , pp. 357 - 364
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Dirscherl, W., Endliche Gruppen mit der Eigenschaft [x, y]x = [x, y]l(x,y) (Diplomarbeit, Würzburg, 1990).Google Scholar
[2]Doerk, K., ‘Minimal nicht überauflösbare, endliche Gruppen’, Math. Z. 91 (1966), 198–205.CrossRefGoogle Scholar
[3]Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, 1967).CrossRefGoogle Scholar