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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Countable closed $ {\rm LFC}$-groups with $ p$-torsion


Author: Felix Leinen
Journal: Trans. Amer. Math. Soc. 336 (1993), 193-217
MSC: Primary 20F24; Secondary 20E22
DOI: https://doi.org/10.1090/S0002-9947-1993-1080170-6
MathSciNet review: 1080170
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Abstract: Let $ LFC$ be the class of all locally $ FC$-groups. We study the existentially closed groups in the class $ LF{C_p}$ of all $ LFC$-groups $ H$ whose torsion subgroup $ T(H)$ is a $ p$-group. Differently from the situation in $ LFC$, every existentially closed $ LF{C_p}$-group is already closed in $ LF{C_p}$, and there exist $ {2^{{\aleph _0}}}$ countable closed $ LF{C_P}$-groups $ G$. However, in the countable case, $ T(G)$ is up to isomorphism always a unique locally finite $ p$-group with similar properties as the unique countable existentially closed locally finite $ p$-group $ {E_p}$.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1080170-6
Article copyright: © Copyright 1993 American Mathematical Society