Small Stable Groups and Generics
Wagner, Frank O.
J. Symbolic Logic, Tome 56 (1991) no. 1, p. 1026-1037 / Harvested from Project Euclid
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We define an $\mathfrak{R}$-group to be a stable group with the property that a generic element (for any definable transitive group action) can only be algebraic over a generic. We then derive some corollaries for $\mathfrak{R}$-groups and fields, and prove a decomposition theorem and a field theorem. As a nonsuperstable example, we prove that small stable groups are $\mathfrak{R}$-groups.
Publié le : 1991-09-15
Classification:  
@article{1183743749,
     author = {Wagner, Frank O.},
     title = {Small Stable Groups and Generics},
     journal = {J. Symbolic Logic},
     volume = {56},
     number = {1},
     year = {1991},
     pages = { 1026-1037},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743749}
}

Wagner, Frank O. Small Stable Groups and Generics. J. Symbolic Logic, Tome 56 (1991) no. 1, pp.  1026-1037. http://gdmltest.u-ga.fr/item/1183743749/