Related papers: Groups which do not admit ghosts

We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a…

Let $p$ be a prime number and suppose that every maximal subgroup of a finite group is either $p$-nilpotent or has prime index. Such group need not be $p$-solvable, and we study its structure by proving that only one nonabelian simple group…

For a finite group $G$, let $p(G)$ denote the minimal degree of a faithful permutation representation of $G$. The minimal degree of a faithful representation of $G$ by quasi-permutation matrices over the fields $\mathbb{C}$ and $\mathbb{Q}$…

For any two degrees coprime to the rank, we construct a family of ring isomorphisms parameterized by GSp(2g) between the cohomology of the moduli spaces of stable Higgs bundles which preserve the perverse filtrations. As consequences, we…

Let $K$ be any field and $G$ be a finite group. Let $G$ act on the rational function field $K(x_g:g\in G)$ by $K$-automorphisms defined by $g\cdot x_h=x_{gh}$ for any $g,h\in G$. Noether's problem asks whether the fixed field…

Let $P$ be a principal indecomposable module of a finite group $G$ in characteristic $2$ and let $\varphi$ be the Brauer character of the corresponding simple $G$-module. We show that $P$ affords a non-degenerate $G$-invariant quadratic…

In this paper, we compute the rational cohomology groups of the classifying space of a simply connected Kac-Moody group of infinite type. The fundamental principle is "from finite to infinite". That is, for a Kac-Moody group G(A) of…

The intrinsic presence of ghosts in the symmetric teleparallel framework is elucidated. We illustrate our general arguments in $f(\mathbb{Q})$ theories by studying perturbations in the three inequivalent spatially flat cosmologies. Two of…

Let K be any field and G be a finite group. Noether's problem asks whether the fixed field is rational (=purely transcendental) over K. We will prove that if G is a non-abelian p-group of order p^n containing a cyclic subgroup of index p…

The subgroup commutativity degree of a group G has been defined in [6] as the probability that two subgroups of G commute, or equivalently that the product of two subgroups is again a subgroup. Problem 4.3 of [6] asks whether there exist…

Let $G$ be a finite group and $V$ be a $G$-representation. We investigate the $RO(G)$-graded Bredon cohomology with constant integral coefficients of the space of ordered configurations in $V$. In the case that $V$ contains a trivial…

We explicitly show that general local higher-derivative theories with only complex conjugate ghosts and normal real particles are unitary at any perturbative order in the loop expansion. The proof presented here relies on integrating the…

We investigate under which circumstances there exists nonzero {\it{projective}} smooth $\field[G]$-modules, where $\field$ is a field of characteristic $p$ and $G$ is a locally pro-$p$ group. We prove the non-existence of (non-trivial)…

We prove that for q\in\C* not a nontrivial root of unity the cohomology group defined by invariant 2-cocycles in a completion of Uq(g) is isomorphic to H^2(P/Q;\T), where P and Q are the weight and root lattices of g. This implies that the…

A group is said to be stable if it is isomorphic to its automorphism group. We investigate how we can extend centerless groups to construct finite stable groups with nontrivial centers. To this end, we classify all finite stable groups…

We study infinite groups interpretable in power bounded $T$-convex, $V$-minimal or $p$-adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups)…

We continue the analysis of the Modular Isomorphism Problem for $2$-generated $p$-groups with cyclic derived subgroup, $p>2$, started in [D. Garc\'ia-Lucas, \'A. del R\'io, and M. Stanojkovski. On group invariants determined by modular…

Given a linear group G over a field k, we define a notion of index and residue of an element g of G(k((t)). This provides an alternative proof of Gabber's theorem stating that G has no subgroups isomorphic to the additive or the commutative…

For a complex algebraic variety $X$, we show that triviality of the sheaf cohomology group $H^0(X,\mathcal{H}^3)$ occurring on the second page of the Bloch-Ogus spectral sequence follows from a condition on the integral Chow group $CH^2X$…

We present a classification of finite $p$-groups $G$ with $\gamma_2(G)$, the commutator subgroup of $G$, of order $p^4$ and exponent $p$ such that not all elements of $\gamma_2(G)$ are commutators.