We embed a countably categorical group G into a locally compact group G with a non-trivial topology and study how topological properties of G are related to the structure of definable subgroups of G. Unauthenticated Download Date | 7/28/18 8:22 AM Lemma 1.1. If G is an o-categorical group, then there is a formula cðx; yÞ such that G cðg; hÞ if and only if h A hgi G . This is a consequence of the fact that G has finite conjugate spread (see [2] ): there exists a number m such that for any g A G

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... ny element of hgi G is a product of at most m conjugates of g e , e A fÀ1; 1g. An important role in our arguments is played by [2, Theorem A], which states that an o-categorical group G has a finite series 1 ¼ G 0 < G 1 < Á Á Á < G n ¼ G with each G i characteristic in G, and with each G i =G iÀ1 either elementary abelian, or isomorphic to some Boolean power P B with P a finite simple non-abelian group and B an atomless Boolean ring, or an o-categorical characteristically simple non-abelian 296 A. Ivanov Unauthenticated Download Date | 7/28/18 8:22 AM