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INJECTORS IN CERTAIN PROFINITE AND LOCALLY FINITE GROUPS

Published online by Cambridge University Press:  01 April 1997

M. J. TOMKINSON
M. J. TOMKINSON
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Abstract

Fitting classes and their associated injectors have been considered in a number of classes of locally finite groups [9, 8, 4, 5]. In particular, Dixon has considered the class [Lfr ] of countable locally finite groups with min −p for all primes p. He has shown that if the [Lfr ]-group G is radical (that is, it has an ascending locally nilpotent series) then G has locally nilpotent injectors, any two of which are isomorphic. Question 7.4.7 in [5] asks whether the restriction of being radical can be removed in this result.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 348 - 356
Copyright
The London Mathematical Society 1997

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