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The Generalized Wielandt Subgroup of a Group

Published online by Cambridge University Press:  20 November 2018

James C. Beidleman
Affiliation:
Department of Mathematics University of Kentucky Lexington, Kentucky 40506-0027 U.S.A
Martyn R. Dixon
Affiliation:
Department of Mathematics University of Alabama Tuscaloosa, Alabama 35487-0350 U.S.A.
Derek J. S. Robinson
Affiliation:
Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, Illinois 61801 U.S.A.
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Abstract

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The intersection IW(G) of the normalizers of the infinite subnormal subgroups of a group G is a characteristic subgroup containing the Wielandt subgroup W(G) which we call the generalized Wielandt subgroup. In this paper we show that if G is infinite, then the structure of IW(G)/ W(G) is quite restricted, being controlled by a certain characteristic subgroup S(G). If S(G) is finite, then so is IW(G)/ W(G), whereas if S(G) is an infinite Prüfer-by-finite group, then IW(G)/W(G) is metabelian. In all other cases, IW(G) = W(G).

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1995

References

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