Related papers: C-Groups

In this paper, we compute the rational cohomology groups of the classifying space of a simply connected Kac-Moody group of infinite type. The fundamental principle is "from finite to infinite". That is, for a Kac-Moody group G(A) of…

Let $\chi$ be an irreducible character of a group $G,$ and $S_c(G)=\sum_{\chi\in {\rm Irr}(G)}{\rm cod}(\chi)$ be the sum of the codegrees of the irreducible characters of $G.$ Write ${\rm fcod} (G)=\frac{S_c(G)}{|G|}.$ We aim to explore…

Consider any sequence of finite groups $A^t$, where $t$ takes values in an integer index set $\mathbf{Z}$. A group system $A$ is a set of sequences with components in $A^t$ that forms a group under componentwise addition in $A^t$, for each…

We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their…

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…

The prime graph $\Gamma(G)$ of a finite group $G$ (also known as the Gruenberg-Kegel graph) has as its vertices the prime divisors of $|G|$, and $p\text-q$ is an edge in $\Gamma(G)$ if and only if $G$ has an element of order $pq$. Since…

We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…

The $G$-graph $\Gamma(G,S)$ is a graph from the group $G$ generated by $S\subseteq G$, where the vertices are the right cosets of the cyclic subgroups $\langle s \rangle, s\in S$ with $k$-edges between two distinct cosets if there is an…

For a finite group $G$, let $LC(G)$ be the subgroup generated by elements $x$ such that, for all $y \in G$ and all integers $n$, the order of $x^n y$ divides the least common multiple of the orders of $x$ and $y$. This subgroup is a…

We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $2^k -1$ for some $k$; or (c) a projective special linear…

The rank of a point-line geometry G is usually defined as the generating rank of G, namely the minimal cardinality of a generating set. However, when the subspace lattice of G satisfies the Exchange Property we can also try a different…

We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first…

We study groups having the property that every non-cyclic subgroup contains its centralizer. The structure of nilpotent and supersolvable groups in this class is described. We also classify finite $p$-groups and finite simple groups with…

A ring $R$ with center $C$ is said to be \textit{centrally essential} if the module $R_C$ is an essential extension of the module $C_C$. In the paper, we study groups whose group algebras over fields are centrally essential rings. We focus…

Let $G$ be a finite almost simple group. It is well known that $G$ can be generated by 3 elements, and in previous work we showed that 6 generators suffice for all maximal subgroups of $G$. In this paper we consider subgroups at the next…

We prove that a finite $3$-group in the Cremona group $\mathrm{Cr}_3(\mathbb{C})$ can be generated by at most $4$ elements. This provides the last missing piece in bounding the ranks of finite $p$-subgroups in the space Cremona group.

Let $RG$ be the gruop ring of the group $G$ over ring $R$ and $\mathscr{U}(RG)$ be its unit group. Finding the structure of the unit group of a finite group ring is an old topic in ring theory. In, G. Tang et al: Unit Groups of Group…

We study the class of pseudocompact C*-algebras, which are the logical limits of finite-dimensional C*-algebras. The pseudocompact C*-algebras are unital, stably finite, real rank zero, stable rank one, and tracial. We show that the…

The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups…

In this article, we study connections between components of the Cayley graph $\mathrm{Cay}(G,A)$, where $A$ is an arbitrary subset of a group $G$, and cosets of the subgroup of $G$ generated by $A$. In particular, we show how to construct…