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Uncountable existentially closed groups in locally finite group classes

Published online by Cambridge University Press:  18 May 2009

Felix Leinen
Felix Leinen
Affiliation:
Fachbereich 17—Mathematik, Johannes Gutenberg Universität, Saarstr. 21, D-6500 Mainz, West Germany.
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In this paper, will always denote a local class of locally finite groups, which is closed with respect to subgroups, homomorphic images, extensions, and with respect to cartesian powers of finite -groups. Examples for x are the classes L ℐπ of all locally finite π-groups and L(ℐπ ∩ ) of all locally soluble π-groups (where π is a fixed set of primes). In [4], a wreath product construction was used in the study of existentially closed -groups (=e.c. -groups); the restrictive type of construction available in [4] permitted results for only countable groups. This drawback was then removed partially in [5] with the help of permutational products. Nevertheless, the techniques essentially only permitted amalgamation of -groups with locally nilpotent π-groups. Thus, satisfactory results could be obtained for Lp-groups (resp. locally nilpotent π-groups) [6], while the theory remained incomplete in all other cases.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 2 , May 1990 , pp. 153 - 163
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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