Countable closed 𝐿𝐹𝐶-groups with 𝑝-torsion

Leinen, Felix

doi:10.1090/S0002-9947-1993-1080170-6

Countable closed $\textrm {LFC}$-groups with $p$-torsion
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Trans. Amer. Math. Soc. 336 (1993), 193-217 Request permission

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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