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Subgroups of locally finite productsof locally nilpotent groups

Published online by Cambridge University Press:  01 October 1999

Burkhard Höfling
Burkhard Höfling
Affiliation:
Mathematisches Institut, Friedrich-Schiller-Universität, D-07740 Jena, Germany. E-mail:hoefling@mathematik.uni-jena.de
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Abstract

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Letthe locally finite group G be the product of two locallynilpotent subgroups A and B, and assume thatH is a subgroup of G belonging to a group classℱ. The question is considered whether thereexists a subgroup X of G containing H whichbelongs to ℱ and satisfies $X=(X\capA)(X\capB)$.Under various assumptions on G and ℱ,necessary and sufficient conditions for the existence of such a subgroupX are obtained.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 3 , October 1999 , pp. 323 - 343
Copyright
1999 Glasgow Mathematical Journal Trust