Related papers: The class $\mathcal{MN}$ of groups in which all ma…
A recurring theme in finite group theory is understanding how the structure of a finite group is determined by the arithmetic properties of group invariants. There are results in the literature determining the structure of finite groups…
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…
The maximal normal subgroup growth type of a finitely generated group is $n^{\log n}$. Very little is known about groups with this type of growth. In particular, the following is a long standing problem: Let $\Gamma$ be a group and $\Delta$…
In this paper, we set $\eta (G)$ to be the number of conjugacy classes of maximal cyclic subgroups of $G$. We consider $\eta$ and direct and semi-direct products. We characterize the normal subgroups $N$ so that $\eta (G/N) = \eta (G)$. We…
A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…
The paper is concerned with maximal subgroups of the ample (better known as topological full) groups of homeomorphisms of totally disconnected compact metrizable topological spaces. We describe all maximal subgroups that are stabilizers of…
Let $G$ be a finite group and $N_{\Omega}(G)$ be the intersection of the normalizers of all subgroups belonging to the set $\Omega(G),$ where $\Omega(G)$ is a set of all subgroups of $G$ which have some theoretical group property. In this…
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…
We conclude from the results of Hanguang Meng and Xiuyun Guo some corollaries about the existence of strictly 2-maximal subgroups in groups. We give examples of groups that illustrate properties of strictly 2-maximal subgroups.
In this paper, we pose the concepts of pre-topological groups and some generalizations of pre-topological groups. First, we systematically investigate some basic properties of pre-topological groups; in particular, we prove that each…
Given a strict partial order $\Delta$ on a set $\Lambda$ and an arbitrary ring $R$ with $1\neq 0$, the corresponding McLain group $M(\Delta)$ has been studied in depth. We construct a larger family of McLain groups $G(\Delta)$, where…
Let $A\subset B$ be an extension of commutative reduced rings and $M\subset N$ an extension of positive commutative cancellative torsion-free monoids. We prove that $A$ is subintegrally closed in $B$ and $M$ is subintegrally closed in $N$…
Gcharacter tables of a finite group G were defined before. These tables can be very useful to obtain certain structural information of a normal subgroup from the character table of G. We analyze certain structural properties of normal…
An inner model M is MINIMAL if there is a class A such that <M,A> is amenable yet has no transitive proper elementary submodel. We study minimal universes in the context of 0#. For example we prove: If 0# exists then there is an inner model…
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
Maximum VC classes which are stable in the sense of model theory are characterized.
The number of subgroups and the number of cyclic subgroups are natural combinatorial invariants of a finite group. We investigate how restrictions on these quantities, together with the number of distinct prime divisors of $|G|$, enforce…
The Andrews-Curtis conjecture remains one of the outstanding open problems in combinatorial group theory. It claims that every normally generating $r$-tuple of a free group $F_r$ of rank $r\geq 2$ can be reduced to a basis by means of…
We prove that a semiregular topological space $X$ is completely regular if and only if its topology is generated by a normal quasi-uniformity. This characterization implies that each regular paratopological group is completely regular. This…