4,171 research outputs found

    New examples of small Polish structures

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    We answer some questions from a paper of Krupi\'nski by giving suitable examples of small Polish structures. First, we present a class of small Polish group structures without generic elements. Next, we construct a first example of a small non-zero-dimensional Polish GG-group

    On \omega-categorical, generically stable groups

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    We prove that each \omega-categorical, generically stable group is solvable-by-finite.Comment: 11 page

    Left-ordered inp-minimal groups

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    We prove that any left-ordered inp-minimal group is abelian, and we provide an example of a non-abelian left-ordered group of dp-rank 2

    Locally finite profinite rings

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    We investigate the structure of locally finite profinite rings. We classify (Jacobson-) semisimple locally finite profinite rings as products of complete matrix rings of bounded cardinality over finite fields, and we prove that the Jacobson radical of any locally finite profinite ring is nil of finite nilexponent. Our results apply to the context of small compact GG-rings, where we also obtain a description of possible actions of GG on the underlying ring.Comment: 17 page
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