arXiv subjects

Ido Karshon

Publications and source records attributed to Ido Karshon.

2 recordsLinked to original sources

arXiv2026

Subgroups with all finite lifts isomorphic are conjugate

We show that for non-conjugate subgroups $G_1$ and $G_2$ of a finite group $G$ there exists an extension of $G$ (by a finite group) in which the pre-images of $G_1$ and $G_2$ are not isomorphic. This allows us to show that $\mathbb Z$-coset equivalent subgroups of a finite group are not necessarily isomorphic, answering a question of Dipendra Prasad. We also indicate connections to profinite rigidity, anabelian geometry, mapping class groups, and non-arithmetic lattices in Lie groups.

math.GR↗

arXiv2026

Pro-$\ell$-by-cyclotomic and tamely ramified variants of the Neukirch-Uchida Theorem

We prove a generalization of the Neukirch-Uchida Theorem. In particular, we show that the isomorphism type of a number field $K$ can be recovered from the maximal pro-$\ell$-by-cyclotomic quotient of its absolute Galois group $G_{\overline{K}/K}$. This should be contrasted with the previous result that the isomorphism type cannot, in general, be recovered from the maximal pronilpotent quotient. We also show that the isomorphism type can be recovered from the maximal tamely ramified quotient.

math.NT↗