相关论文: Transformation Digroups

Working in the soft-element (classical) viewpoint, we introduce \emph{soft bitopological groups}: soft groups endowed with two soft topologies such that the induced topologies on the set of soft elements make the soft-element group into a…

A profinite group equipped with an expansive endomorphism is equivalent to a one-sided group shift. We show that these groups have a very restricted structure. More precisely, we show that any such group can be decomposed into a finite…

We give a solution to Dehn's isomorphism problem for the class of all hyperbolic groups, possibly with torsion. We also prove a relative version for groups with peripheral structures. As a corollary, we give a uniform solution to…

It is shown that each integrable mapping is connected with a hierarchical completely integrable sytem of equations of evolution type which are invariant with respect to the transformation described by this mapping.

We prove the even isomorphism theorem for Coxeter groups

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…

In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.

We develop a general deformation theory of objects in homotopy and derived categories of DG categories. The main result is a general pro-representability theorem for the corresponding deformation functor.

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…

We prove an upper bound for the number of cyclic transitive subgroups in a finite permutation group and clarify the structure of the groups for which this bound becomes sharp. We also give an application in the theory of number fields.

We show that a quotient group of a CI-group with respect to (di)graphs is a CI-group with respect to (di)graphs.

It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.

Greenberg proved that every countable group $A$ is isomorphic to the automorphism group of a Riemann surface, which can be taken to be compact if $A$ is finite. We give a short and explicit algebraic proof of this for finitely generated…

Let $X$ be a nonempty set and $T(X)$ the full transformation semigroup on $X$. For any equivalence relation $E$ on $X$, define a subsemigroup $T_{E^*}(X)$ of $T(X)$ by $$ T_{E^*}(X)=\{\alpha\in T(X):\text{for all}\ x,y\in X, (x,y)\in…

We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.

In this paper, we prove that the fundamental group of a simplicial complex is isomorphic to the algebraic fundamental group of its incidence algebra, and we derive some applications.

In this article, we develop the basic theory of digital topological groups. The basic definitions directly lead to two separate categories, based on the details of the continuity required of the group multiplication. We define $\NP_1$- and…