Related papers: Equivalents of NOTOP

Let $\alpha$ be a coprime automorphism of a group $G$ of prime order and let $P$ be an $\alpha$-invariant Sylow $p$-subgroup of $G$. Assume that $p\notin \pi(C_G(\alpha))$. Firstly, we prove that $G$ is $p$-nilpotent if and only if…

For an arbitrary field $K$ and $K$-variety $V$, we introduce the \'etale-open topology on the set $V(K)$ of $K$-points of $V$. This topology agrees with the Zariski topology, Euclidean topology, or valuation topology when $K$ is separably…

We introduce tools from discrete convexity theory and polyhedral geometry into the theory of West's stack-sorting map $s$. Associated to each permutation $\pi$ is a particular set $\mathcal V(\pi)$ of integer compositions that appears in a…

Let $R$ be a Noetherian $\mathbb{N}$-graded ring. Let $L$, $M$ and $N$ be finitely generated graded $R$-modules with $N \subseteq M$. For a homogeneous ideal $I$, and for each fixed $k \in \mathbb{N}$, we show the asymptotic linearity of…

A loop is automorphic if its inner mappings are automorphisms. Using so-called associated operations, we show that every commutative automorphic loop of odd prime power order is centrally nilpotent. Starting with anisotropic planes in the…

We study classes of atomic models At_T of a countable, complete first-order theory T . We prove that if At_T is not pcl-small, i.e., there is an atomic model N that realizes uncountably many types over pcl(a) for some finite tuple a from N,…

We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in $v_n$-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen's results in…

If for any $k$ the $k$-th coefficient of a polynomial I(G;x) is equal to the number of stable sets of cardinality $k$ in the graph $G$, then it is called the independence polynomial of $G$ (Gutman and Harary, 1983). Let $a$ be the size of a…

We study finitely generated models of countable theories, having at most countably many nonisomorphic finitely generated models. We intro- duce a notion of rank of finitely generated models and we prove, when T has at most countably many…

We prove that in a countable theory $T$ fully stable over a predicate $P$, any $\lam$-complete set $A$ has the $\lam$-existence property. This means that $A$ can be extended to a $\lam$-saturated model of $T$ without changing the $P$-part.…

A theory is NIP (resp. stable) if and only if every formula with parameters in two single variables is NIP (resp. does not have the order property).

We compare two approaches to the homotopy theory of infinity-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets and infinity-categories which replaces simplices by trees. The other…

An algebraic process for the construction of an autotopism for a non-Steiner C-loop is described and this is demonstrated with an example using a known finite C-loop. In every C-loop, two of its parastrophes are not equivalent(equal) it, if…

We seek progress in the study of subtoposes of the effective topos. First we treat Van Oosten's result that local operators on the effective topos are internally NNO-indexed joins of what we shall call 'basic' local operators. Our main…

A strong antidiamond principle (*c) is shown to be consistent with CH. This principle can be stated as a "P-ideal dichotomy": every P-ideal on omega-1 (i.e. an ideal that is sigma-directed under inclusion modulo finite) either has a closed…

We call a reductive complex group $G$ quasi-toral if $G^0$ is a torus. Let $G$ be quasi-toral and let $V$ be a faithful $1$-modular $G$-module. Let $N$ (the shell) be the zero fiber of the canonical moment mapping $\mu\colon V\oplus…

Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C_{p^\infty}$. We show that if $G$ is nilpotent, then the…

We provide several crucial technical extensions of the theory of stable independence notions in accessible categories. In particular, we describe circumstances under which a stable independence notion can be transferred from a subcategory…

Theorem (after Giraud, SGA 4): Suppose $A$ is a simplicial category. The following conditions are equivalent: (i) There is a cofibrantly generated closed model category $M$ such that $A$ is equivalent to the Dwyer-Kan simplicial…

We present a new proof of descent for stably dominated types in any theory, dropping the hypothesis of the existence of global invariant extensions. Additionally, we give a much simpler proof of descent for stably dominated types in…