# Tag Info

### A Shelah group in ZFC?

This is a partial answer to Problem 2 about the largest number $n$ such that every $n$-Shelah group is finite. The main result of this paper implies that this number $n<36$, at least under the ...
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Accepted

Yes. Nilpotency of $T$ is not needed. Assume that $N_G(P_s)>P_s$. Then for some $i<s$, $N_G(P_s)$ has a Sylow $p_i$-subgroup $Q_i\ne 1$. Assume without loss that $p_i$ divides $|H|$. Then $... • 2,344 1 vote Accepted ### The dimension of a torsion-free$p$-adic analytic group generated by two generators A pro-$p$group$G$has$\textit{lower rank}r$if$r$is minimal such that every open subgroup of$G$contains an open subgroup generated by at most$r$elements. Lubotzky and Mann showed that the ... • 5,008 1 vote ### Schur multiplier of$\mathrm{SL}(2,\mathbb{Q})\DeclareMathOperator\SL{SL}\DeclareMathOperator\Sp{Sp}$For a field$F$with$|F|>4$and$|F|\neq9$, the group$H_2(\SL_2(F))$has a presentation in terms of the symplectic Steinberg symbols; that ... • 329 1 vote Accepted ### A group-theoretic lemma in a paper by Ershov and He Here is @AndyPutman's comment as an answer (so that it can be accepted), made CW to avoid reputation. If @AndyPutman prefers to post the answer, then I will delete this. This only needs the fact ... 1 vote Accepted ### A result of Borel on extensions of arithmetic groups A proof appears in Section 2.3 of my paper Mapping class groups of manifolds with boundary are of finite type. As pointed out in the comments, it is crucial that$G$is unipotent. • 7,668 1 vote Accepted ### On the number$n_0$in Shelah's construction of a Jonsson group The number$n_0$in Shelah's proof equals$6640$, but can be lowered (by a minor modification of his method) to$36\$, see this preprint.
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