Search results for "Existentially closed model"

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Uncountable existentially closed groups in locally finite group classes

1990

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 per…

Pure mathematicsProfinite groupLocally finite groupGeneral MathematicsUncountable setClassification of finite simple groupsCA-groupExistentially closed modelMathematicsGlasgow Mathematical Journal
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Existentially closed central extensions of locally finite p-groups

1986

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

Discrete mathematicsClass (set theory)NoticeGeneral MathematicsAbelian groupPrime (order theory)MathematicsExistentially closed modelMathematical Proceedings of the Cambridge Philosophical Society
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