Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations

Leinen, Felix; Puglisi, Orazio

doi:10.1090/S0002-9947-99-02309-0

Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations
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by Felix Leinen and Orazio Puglisi

Trans. Amer. Math. Soc. 352 (2000), 1913-1934

DOI: https://doi.org/10.1090/S0002-9947-99-02309-0

Published electronically: December 10, 1999

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Abstract:

Let $\mathfrak {X}$ be either the class of all transitive groups of finitary permutations, or the class of all periodic irreducible finitary linear groups. We show that almost primitive $\mathfrak {X}$-groups are countably recognizable, while totally imprimitive $\mathfrak {X}$-groups are in general not countably recognizable. In addition we derive a structure theorem for groups all of whose countable subsets are contained in totally imprimitive $\mathfrak {X}$-subgroups. It turns out that totally imprimitive $p$-groups in the class $\mathfrak {X}$ are countably recognizable.

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