Geodesic
Uncountable existentially closed groups in locally finite group classes
Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 153-163

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Leinen, Felix. Uncountable existentially closed groups in locally finite group classes. Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 153-163. doi: 10.1017/S0017089500009174
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