Related papers: On some examples of group actions and group extens…
This paper studies properties of entropy functions that are induced by groups and subgroups. We showed that many information theoretic properties of those group induced entropy functions also have corresponding group theoretic…
We prove several extensions of the Erdos-Fuchs theorem.
Given a partial action $\alpha=(A_g,\alpha_g)_{g\in \mathcal{G}}$ of a connected groupoid $\mathcal{G}$ on a ring $A$ and an object $x$ of $\mathcal{G}$, the isotropy group $\mathcal{G}(x)$ acts partially on the ideal $A_x$ of $A$ by the…
We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acts absolutely non-freely on the boundary of the…
We define orbifold mapping class groups (with marked points) and study them using their action on certain orbifold analogs of arcs and simple closed curves. Moreover, we establish a Birman exact sequence for suitable subgroups of orbifold…
Extensions of a direct product T of two cyclic groups Z_n1 and Z_n2 by an Abelian (gauge) group G with the trivial action of T on G are considered. All possible (nonequivalent) factor systems are determined using the Mac Lane method. Some…
We introduce and study expansions of real numbers with respect to two integer bases.
We classify crossed product gradings for arbitrary groups and fields up to several equivalence relations in terms of group actions and their orbits.
We study expressive power of continuous logic in classes of metric groups defined by properties of their actions. For example we consider properties non-OB, non-FH and non-FR. The paper substantially extends Section 2 of the paper A.Ivanov,…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.
We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative…
For two countably infinite fields whose multiplicative groups are isomorphic, we examine invariant couplings between the actions that these groups induce on the additive Pontryagin duals of the fields. We show that the actions are disjoint…
We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.
Let k be an algebraically closed field of characteristic p>0 and C a connected nonsingular projective curve over k with genus g>1. Let (C,G) be a "big action", i.e. a pair (C,G) where G is a p-subgroup of the k-automorphism group of C such…
The aim of this paper is to study co-prolongations of central extensions. We construct the obstruction theory for co-prolongations and classify the equivalence classes of these by kernels of a homomorphisms between 2-dimensional cohomology…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
We give a characterisation of central extensions of a Lie group G by the non-zero complex numbers in terms of a differential two-form on G and a differential one-form on GxG. This is applied to the case of the central extension of the loop…
We investigate the isolated points in the space of finitely generated groups. We give a workable characterization of isolated groups and study their hereditary properties. Various examples of groups are shown to yield isolated groups. We…
All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.