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Let $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer…

Representation Theory · Mathematics 2011-12-02 Tiberiu Coconet

For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces are a convenient language for describing structures equipped with a family of equivalence relations. When $\Lambda$ is finite and distributive, there exists a generic…

Logic · Mathematics 2025-11-21 Samuel Braunfeld

We show that in algebraically locally finite countable homogeneous structures with a free stationary independence relation the small index property implies the strong small index property. We use this and the main result of [15] to deduce…

Logic · Mathematics 2018-10-05 Gianluca Paolini , Saharon Shelah

We describe an evolving and conjectural extension of the Langlands program for a class of nonlinear covering groups of algebraic origin studied by Brylinski-Deligne. In particular, we describe the construction of an L-group extension of…

Number Theory · Mathematics 2014-09-17 Wee Teck Gan , Fan Gao

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more…

q-alg · Mathematics 2008-11-26 K. Bresser , A. Dimakis , F. Mueller-Hoissen , A. Sitarz

The ultraproduct construction is generalized to $p$-ultramean constructions ($1\leqslant p<\infty$) by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments $\mathscr L^p$ of…

Logic · Mathematics 2019-10-03 Seyed-Mohammad Bagheri

We study the problem of extending partial isomorphisms for hypertournaments, which are relational structures generalizing tournaments. This is a generalized version of an old question of Herwig and Lascar. We show that the generalized…

Logic · Mathematics 2018-09-19 Jingyin Huang , Michael Pawliuk , Marcin Sabok , Daniel Wise

We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define…

Logic · Mathematics 2023-08-09 Nadav Meir

We prove several structural results on definably compact groups G in o-minimal expansions of real closed fields, such as (i) G is definably an almost direct product of a semisimple group and a commutative group, and (ii) the group (G, .) is…

Logic · Mathematics 2008-11-04 Ehud Hrushovski , Ya'acov Peterzil , Anand Pillay

Let L be a countable and locally finite CW complex. Suppose that the class of all metrizable compacta of extension dimension not greater than L contains a universal element which is an absolute extensor in dimension L. Our main result shows…

Geometric Topology · Mathematics 2007-05-23 Alex Karasev , Vesko Valov

Consider a finitely generated group $G$ that is relatively hyperbolic with respect to a family of subgroups $H_1, ..., H_n$. We present an axiomatic approach to the problem of extending metric properties from the subgroups $H_i$ to the full…

Group Theory · Mathematics 2019-07-17 Daniel A. Ramras , Bobby W. Ramsey

We consider associative algebras L over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this relative and split…

K-Theory and Homology · Mathematics 2007-05-23 Claude Cibils , Eduardo Marcos , Maria Julia Redondo , Andrea Solotar

In this paper, we first get a criterion formula for whether a differential form is holomorphic with respect to the generalized complex structure induced by $\epsilon$. Next, we get the local extensions of $\overline\partial$-closed forms on…

Differential Geometry · Mathematics 2018-03-13 Kang Wei

We introduce relational semantics for "flat Heyting-Lewis logic" $\mathsf{HLC}^{\flat}$. This logic arises as the extension of intuitionistic logic with a Lewis-style strict implication modality that, contrary to its "sharp" counterpart…

Logic · Mathematics 2026-03-31 Jim de Groot , Tadeusz Litak

In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: (i) L is quasi-finite. (ii) There exists a [L]-invertible…

Geometric Topology · Mathematics 2007-05-23 A. V. Karasev

In this article we prove that every isometric copy of C(L) in C(K) is complemented if L is compact Hausdorff of finite height and K is a compact Hausdorff space satisfying the extension property, i.e., every closed subset of K admits an…

Functional Analysis · Mathematics 2013-10-16 Claudia Correa , Daniel V. Tausk

We introduce Hom-actions, semi-direct product and establish the equivalence between split extensions and the semi-direct product extension of Hom-Leibniz algebras. We analyze the functorial properties of the universal ({\alpha})-central…

Rings and Algebras · Mathematics 2013-09-23 J. M. Casas , N Pacheco Regon

We establish the following model-theoretic characterization: profinite $L$-structures, the cofiltered limits of finite $L$-structures,are retracts of ultraproducts of finite $L$-structures. As a consequence, any elementary class of…

Logic · Mathematics 2007-05-23 Hugo Luiz Mariano

Let $L/K$ be a finite Galois extension whose Galois group $G$ is non-abelian and characteristically simple. Using tools from graph theory, we shall give a closed formula for the number of Hopf-Galois structures on $L/K$ with associated…

Group Theory · Mathematics 2019-10-09 Cindy Tsang

A structure is called homogeneous if every isomorphism between finitely induced substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of…

Combinatorics · Mathematics 2009-12-31 Dragan Mašulović , Rajko Nenadov , Nemanja Škorić