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Finite varieties and groups with Sylow p-subgroups of low class

Part of: Representation theory of groups Structure and classification of infinite or finite 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 finite variety is a class of finite groups closed under taking subgroups, factor groups and finite direct products. To each such class there exists a sequence w1, w2,… of words such that the finite group G belongs to the class if and only if wk(G) = 1 for almost all k. As an illustration of the theory we shall present sequences of words for the finite variety of groups whose Sylow p-subgroups have class c for c = 1 and c = 2.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20E10: Quasivarieties and varieties of groups 20F12: Commutator calculus

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 4 , December 1981 , pp. 464 - 469
Copyright
Copyright © Australian Mathematical Society 1981

References

Brandl, R. (to appear), Zur Theorie der untergruppenabgeschlossenen Formationen: Endliche Varietäten, J. Algebra.Google Scholar
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Walter, J. (1969), ‘The characterization of finite groups with abelian Sylow 2-subgroups’, Ann. of Math. (2) 89, 405–514.CrossRefGoogle Scholar