My motivation for this question is similar to the one in this question. However, that question only asks about the possibility of an infinite $\mathbb F_2$-vector space having trivial automorphism group. What other finite automorphism groups can occur? In particular, can $\mathbb Z/(3)$ occur? (see also this question for extra motivation).
2026-03-30 10:13:20.1774865600
Without choice, what can be the (finite) automorphism groups of $\mathbb F_2$-vector spaces?
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The question about $\mathbb{Z}/3\mathbb{Z}$ is answered (positively) by Andreas Blass in this MathOverflow answer.