相关论文: Subgroups of the Group of Formal Power Series with…

In this note we show that groups with definable generics in a separably closed valued of finite imperfection degree can be embedded into groups definable in their algebraic closure.

In this paper we introduce and study the notion of dynamical forcing. Basically, we develop a toolkit of techniques to produce finitely presented groups which can only act on the circle with certain prescribed dynamical properties. As an…

Just infinite groups play a significant role in profinite group theory. For each $c \geq 0$, we consider more generally JNN$_c$F profinite (or, in places, discrete) groups that are Fitting-free; these are the groups $G$ such that every…

This paper is concerned with absolutely irreducible quasisimple subgroups $G$ of a finite general linear group $GL_d(\mathbb{F}_q)$ for which some element $g\in G$ of prime order $r$, in its action on the natural module…

We describe an algorithm for deciding whether or not a given finitely generated torsion-free nilpotent group is decomposable as the direct product of nontrivial subgroups.

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

In this paper, we study nilpotent $\mathbb{Q}$$[x]$-powered groups that satisfy the following property: For some set of primes $\omega$ in $\mathbb{Q}$$[x]$, every $\omega '$-isolated $\mathbb{Q}$$[x]$-subgroup in some family of its…

We refine Feighn--Handel's results on subgroups of mapping tori of free groups to the special case of free-by-cyclic groups. We use these refinements to show that any finitely generated free-by-cyclic group embeds in a {finitely generated…

The power graph of a group $G$ is the graph whose vertex set is $G$ and two distinct vertices are adjacent if one is a power of the other. This paper investigates the minimal separating sets of power graphs of finite groups. For power…

The enhanced power graph, $\mathcal{E}(G)$, of a group $G$ has vertex set $G$ and two elements are adjacent if they generate a cyclic subgroup. In the case of finite groups, we identify some striking and unexpected properties of these…

The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…

In this paper we classify all capable finite $p$-groups with derived subgroup of order $p$ and $G/G'$ of rank $n-1$.

In this paper we describe finitely generated groups $H$ universally equivalent (with constants from $G$ in the language) to a given torsion-free relatively hyperbolic group $G$ with free abelian parabolics. It turns out that, as in the free…

We show that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup.

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

The paper provides a necessary and sufficient condition for the composition of multivariable formal power series and present the Generalized Chain Rule for formal power series of multiple variables.

Let F be an infinitely generated free group and R a fully invariant subgroup of F such that (a) R is contained in the commutator subgroup F' of F and (b) the quotient group F/R is residually torsion-free nilpotent. Then the automorphism…

The power graph $\mathcal P_G$ of a finite group $G$ is the graph with the vertex set $G$, where two elements are adjacent if one is a power of the other. We first show that $\mathcal P_G$ has an transitive orientation, so it is a perfect…

We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…

We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…