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The Schur-Zassenhaus theorem in locally finite groups

Published online by Cambridge University Press:  09 April 2009

B. Hartley
B. Hartley
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, England.
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Abstract

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Let L = HK be a semidirect product of a normal locally finite π′-group H by a locally finite π′-group K, where π, is a set of primes. Suppose CK(H) = 1 and L is Sylow π-sparse (which in the countable case just says that the Sylow π-subgroups of L are conjugate). This paper completes the characterization of those groups which can occur as K—this had previously been obtained under the assumption that L is locally soluble. The answer is the same—essentially that the groups occurring are those having a subgroup of finite index which is a subdirect product of so-called “pinched” groups.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 4 , December 1976 , pp. 491 - 493
Copyright
Copyright © Australian Mathematical Society 1976

References

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