Related papers: String C-group representations of almost simple gr…

This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…

This is a survey article on selected topics in approximation theory. The topics either use techniques from the theory of several complex variables or arise in the study of the subject. The survey is aimed at readers having an acquaintance…

The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…

The study of string C-group representations of rank at least $n/2$ for the symmetric group $S_n$ has gained a lot of attention in the last fifteen years. In a recent paper, Cameron et al. gave a list of permutation representation graphs of…

Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…

We present new algorithms to classify all string C-group representations of a given group $G$. We use these algorithms to classify all string C-group representations of the sporadic groups of Suzuki and Rudvalis.

In this paper we give a non-computer-assisted proof of the following result: if $G$ is an even transitive group of degree $11$ and has a string C-group representation with rank $r\in\{4,5\}$ then $G\cong\PSL_2(11)$. Moreover this string…

This survey aims to give an overview of several substantial developments of the last 50 years in the structure theory of regular semigroups and to shed light on their impact on other parts of semigroup theory.

We use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of…

In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…

We show that a rank reduction technique for string C-group representations first used for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on…

In this paper we address the issue of existence of cusp forms for almost simple Lie groups using the approach of the second author combined with local information on supercuspidal representations for $p$-adic groups known by the first…

A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a…

We determine the ranks of string C-group representations of the groups ${\rm PSp}(4,\mathbb{F}_q)\cong\Omega(5,\mathbb{F}_q)$, and comment on those of higher-dimensional symplectic and orthogonal groups.

This paper investigates the critical group of a faithful representation of a finite group. It computes the order of the critical group in terms of the character values, and gives some restrictions on its subgroup structure. It also computes…

In this paper, string C-groups of all ranks $3 \leq r \leq \frac{n}{2}$ are provided for each alternating group $A_n$, $n \geq 12$. As the string C-group representations of $A_n$ have also been classified for $n \leq 11$, and it is known…

We give a rank augmentation technique for rank 3 string C-group representations of the symmetric group $S_n$ and list the hypotheses under which it yields a valid string C-group representation of rank 4 thereof.

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.

The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.