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Finitely valued commutator sequences

Published online by Cambridge University Press:  09 April 2009

Reinhold Baer
Reinhold Baer
Affiliation:
8053 Zürich, Eierbrechtstr. 29, Switzerland
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If x and y are elements in the group G, then we denote their commutator by x o y = x-1y-1 = x-1xy; and x o G is the set of all commutators x o g with g ∈ G. A G-commutator sequence is a series of elements ci ∈ G with c1 + 1 ∈ ci O G. Slightly generalizing well known results one proves that the hypercenter of the group G is exacly the set of all elements h ∈ G with the property: every G-commutator sequence, containing h, contains 1 [Proposition 1.1].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 1 , February 1974 , pp. 35 - 80
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Baer, Reinhold, ‘The hypercenter of a group’, Acta Math. 89 (1953), 165–208.CrossRefGoogle Scholar
[2]Baer, Reinhold, ‘Das Hyperzentrum einer Gruppe. III’, Math. Zeitschr. 59 (1953), 292–338.CrossRefGoogle Scholar
[3]Baer, Reinhold, ‘Auflösbare Gruppen mit Maximalbedingung’, Math. Ann. 129 (1955), 139–173.CrossRefGoogle Scholar
[4]Baer, Reinhold, ‘Noethersche Gruppen’, Math. Zeitschr. 66 (1957), 269–288.CrossRefGoogle Scholar
[5]Baer, Reinhold, ‘Lokal Noethersche Gruppen’, Math. Zeitschr. 66 (1957), 341–363.CrossRefGoogle Scholar
[6]Hall, P. and Hartley, B., ‘The stability group of a series of subgroups’, Proc. London Math. Soc. 16 (1966), 1–39.CrossRefGoogle Scholar
[7]Hall, P. and Kulatilaka, C. R., ‘A property of locally finite groups’, Journal London. Math. Soc. 39 (1964), 235–239.CrossRefGoogle Scholar
[8]Huppert, B., Endliche Gruppen I (Springer Verlag; Berlin-Heidelberg-New York 1967).CrossRefGoogle Scholar
[9]Kegel, Otto H. and Wehrfritz, Bertram A. F., Locally Finite Groups (North Holland 1973).Google Scholar
[10]Kurosh, A. G., The Theory of Groups. II. 2nd ed. (Translated and edited by Hirsch, K. A., Chelsea, New York, 1960).Google Scholar
[11]Specht, Wilhelm, Gruppentheorie (Springer Verlag; Berlin-Göttingen-Heidelberg 1956).Google Scholar