Zobrazeno 1 - 10
of 441
pro vyhledávání: '"Thom, Andreas"'
Autor:
Alekseev, Vadim, Thom, Andreas
We show that there are $2^{\aleph_0}$ non-isomorphic universal sofic groups. This proves a conjecture of Simon Thomas.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2406.06741
Autor:
Gohla, Lukas, Thom, Andreas
For $d \geq 4$ and $p$ a sufficiently large prime, we construct a lattice $\Gamma \leq {\rm PSp}_{2d}(\mathbb Q_p),$ such that its universal central extension cannot be sofic if $\Gamma$ satisfies some weak form of stability in permutations. In the p
Externí odkaz:
http://arxiv.org/abs/2403.09582
We study mixed identities for oligomorphic automorphism groups of countable relational structures. Our main result gives sufficient conditions for such a group to not admit a mixed identity without particular constants. We study numerous examples and
Externí odkaz:
http://arxiv.org/abs/2401.09205
We study the word image of words with constants in ${\rm GL}(V)$ and show that it is large provided the word satisfies some natural conditions on its length and its critical constants. There are various consequences: We prove that for every $l \geq 1
Externí odkaz:
http://arxiv.org/abs/2311.03981
In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply that the sub
Externí odkaz:
http://arxiv.org/abs/2309.08400
We show that for any finite-rank free group $\Gamma$, any word-equation in one variable of length $n$ with constants in $\Gamma$ fails to be satisfied by some element of $\Gamma$ of word-length $O(\log (n))$. By a result of the first author, this log
Externí odkaz:
http://arxiv.org/abs/2306.15370
We prove that there exists a constant $c>0$ such that any finite group having no non-trivial mixed identity of length $\leq c$ is an almost simple group with a simple group of Lie type as its socle. Starting the study of mixed identities for almost s
Externí odkaz:
http://arxiv.org/abs/2306.14532
In this note we state a conjecture that characterizes unital C*-algebras for which the unitary group is amenable as a topological group in the norm topology. We prove the conjecture for simple, separable, stably finite, unital, $\mathcal Z$-stable, U
Externí odkaz:
http://arxiv.org/abs/2305.13181
Autor:
Ando, Hiroshi, Thom, Andreas
Let $G$ be a Polish group and let $H \leq G$ be a compact subgroup. We prove that there exists a Borel set $T \subset G$ which is simultaneously a complete set of coset representatives of left and right cosets, provided that a certain index condition
Externí odkaz:
http://arxiv.org/abs/2305.02612
We study the question whether copies of $S^1$ in $\mathrm{SU}(3)$ can be amalgamated in a compact group. This is the simplest instance of a fundamental open problem in the theory of compact groups raised by George Bergman in 1987. Considerable comput
Externí odkaz:
http://arxiv.org/abs/2304.08365