Related papers: Identifying normal and congruence subgroups

We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of numerical semigroups are defined giving a classification of…

We give an algorithm for finding the index of a positive outer automorphism of the free group, and prove the algorithm exits in a finite time.

In this article we consider sheaf quotients of affine superschemes by affine supergroups that act on them freely. The necessary and sufficient conditions for such quotients to be affine are given. If $G$ is an affine supergroup and $H$ is…

Subgroup discovery is a local pattern mining technique to find interpretable descriptions of sub-populations that stand out on a given target variable. That is, these sub-populations are exceptional with regard to the global distribution.…

A finitely generated group admits a decomposition, called its Grushko decomposition, into a free product of freely indecomposable groups. There is an algorithm to construct the Grushko decomposition of a finite graph of finite rank free…

We show that a differential algebraic group can be filtered by a finite subnormal series of differential algebraic groups such that successive quotients are almost simple, that is have no normal subgroups of the same type. We give a…

We prove that the completed cohomology groups of SL_N(Z) in fixed degree stabilize as N goes to infinity. We also prove that the action of Hecke operators on stable cohomology is trivial, in a precisely defined sense.

A subgroup of a group is contranormal if its normal closure coincides with the group. We call such groups without proper contranormal subgroups contranormal-free. In this paper we prove various results concerning contranormal-free groups…

These notes present two normal surface theory algorithms to detect the unknot and use the split-link algorithm to prove that the figure-eight knot is knotted.

This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of…

In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.

We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.

The Hecke category is bigraded. For completeness, we classify gradings on the Hecke category. We also classify object-preserving autoequivalences.

We give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers. This gives further insight into the structure lattices of branch groups introduced by the second author.…

The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.

We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group $G$ is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of $G$. We also provide a…

It is proved that any family of analytic functions with spherical derivative uniformly bounded away from zero ist normal.

We study the class of finite groups $G$ satisfying $\Phi (G/N)= \Phi(G)N/N$ for all normal subgroups $N$ of $G$. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe…

We consider whether given a simple, finite description of a group in the form of an algorithm, it is possible to algorithmically determine if the corresponding group has some specified property or not. When there is such an algorithm, we…

Every two-sided ideal $\mathfrak a$ in the integral group ring $\mathbb Z[G] $ of a group $G$ determines a normal subgroup $G \cap (1 + \mathfrak a)$ of $G$. In this paper certain problems related to the identification of such subgroups,…