Related papers: A co-analytic Cohen indestructible maximal cofinit…

Let G be a connected reductive group over an algebraic closure of a finite field Fq. In this paper it is proved that the infinite dimensional Steinberg module of kG defined by N. Xi in 2014 is irreducible when k is a field of positive…

If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K…

We prove the following result which is due to the third author. Let $n \geq 1$. If $\boldsymbol\Pi^1_n$ determinacy and $\Pi^1_{n+1}$ determinacy both hold true and there is no $\boldsymbol\Sigma^1_{n+2}$-definable $\omega_1$-sequence of…

In this article we extend independent results of Lusztig and H\'ezard concerning the existence of irreducible characters of finite reductive groups, (defined in good characteristic and arising from simple algebraic groups), satisfying a…

We use a constructive method to obtain all but finitely many p-local representation zeta functions of a family Mn of finitely generated nilpotent groups with maximal nilpotency class. For representation dimensions coprime to all primes p <…

Using a theorem from pcf theory, we show that for any singular cardinal nu, the product of the Cohen forcing notions on kappa, kappa < nu adds a generic for the Cohen forcing notion on nu^+. This solves Problem 5.1 in Miller's list…

Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $\pi$ an irreducible admissible representation of $G$. In this article we prove a necessary and sufficient condition for the finiteness of the multiplicities of $L$-types…

We find the exact size of a maximal non-commuting set in unipotent uppertriangular linear group $UU_4(\mathbb{F}_q)$ in terms of a non-commuting geometric structure (Refer Definition [10]), where $\mathbb{F}_q$ is the finite field with $q$…

We show that it is consistent relative to ZF, that there is no well-ordering of $\mathbb{R}$ while a wide class of special sets of reals such as Hamel bases, transcendence bases, Vitali sets or Bernstein sets exists. To be more precise, we…

We prove that for lambda = beta_omega or just lambda strong limit singular of cofinality aleph_0, if there is a universal member in the class K^lf_lambda of locally finite groups of cardinality lambda, then there is a canonical one…

We say a group is finitely annihilated if it is the set-theoretic union of all its proper normal finite index subgroups. We investigate this new property, and observe that it is independent of several other well known group properties. For…

We (a) prove that continuous morphisms from locally compact groups to locally exponential (possibly infinite-dimensional) Lie groups factor through Lie quotients, recovering a result of Shtern's on factoring norm-continuous representations…

We show that any stochastically monotone Feller semigroup on R can be extended by a consistent family of order-preserving Feller semigroups on the successive powers of R. We exhibit a specific such family, which is uniquely characterized by…

We prove that compact complex manifolds bearing a holomorphic Riemannian metric have infinite fundamental group.

We study $\Sigma_1(\omega_1)$-definable sets (i.e. sets that are equal to the collection of all sets satisfying a certain $\Sigma_1$-formula with parameter $\omega_1$) in the presence of large cardinals. Our results show that the existence…

The well-known Eckmann-Hilton Principle may be applied to prove that fundamental groups of $H$-spaces are commutative. In this paper, we identify an infinitary analogue of the Eckmann-Hilton Principle that applies to fundamental groups of…

We construct countable groups $G$ with the following new degree of W*-superrigidity: if $L(G)$ is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra $L(\Lambda)$, then the groups…

For any odd prime $p$ and any imaginary quadratic field $K$, the $p$-tower group $G_K$ associated to $K$ is the Galois group over $K$ of the maximal unramified pro-$p$-extension of $K$. This group comes with an action of a finite group…

In relation to Kostant's problem for simple highest weight modules over the general linear Lie algebra, we prove a persistence result for Kostant negative consecutive patterns. Inspired by it, we introduce the notion of a Kostant cuspidal…

We prove that over an algebraically closed field of characteristic $p>0$ there are exactly, up to isomorphism, $n$ infinitesimal commutative unipotent $k$-group schemes of order $p^n$ with one-dimensional Lie algebra, and we explicitly…