相关论文: A Package of Programs for Determination of Some Cl…

In this paper we introduce and study the concept of normality degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be normal. Explicit formulas are obtained for some particular classes of…

We show that in the extended modular group PGL(2,Z) there are exactly seven finite subgroups up to conjugacy; three subgroups of size 2, one subgroup each of size 3, 4, and 6, and the trivial subgroup of size 1.

This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented.

We give a description of finitely generated prosoluble subgroups of the profinite completion of $3$-manifold groups and virtually compact special groups.

This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

A collection C of subgroups of a finite group G can give rise to three different standard formulas for the cohomology of G in terms of either: the subgroups in C; or their centralizers; or their normalizers. We give a short but systematic…

We give several algorithms addressing computations of intersections of conjugate subgroups.

In this note, we study the finite groups with the number of cylic subgroups no greater than 6.

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…

We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special…

We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan…

Computations in the cohomology of finite groups.

Motivated by the need for efficient isomorphism tests for finite groups, we present a polynomial-time method for deciding isomorphism within a class of groups that is well-suited to studying local properties of general finite groups. We…

Consider a relatively hyperbolic group G. We prove that if G is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of G, a solution of its…

We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…

A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes.…

We describe finite soluble groups in which every $n$-maximal subgroup is $\mathfrak F$-subnormal.