Related papers: On Reid's recipe for non abelian groups

For any finite subgroup G in SL3(C), work of Bridgeland-King-Reid constructs an equivalence between the G-equivariant derived category of C^3 and the derived category of the crepant resolution Y = G-Hilb(C^3) of C^3/G. When G is abelian we…

Let $X=GD$ be a group, where $G$ is a nonabelian simple group and $D$ is a dihedral group. These groups $X$ are closely related to regular Cayley maps. The main theorems of this paper describes $X$.

This is an expository work presenting in detail the proof of the structure theorem for divisible abelian groups. A divisible abelian group is an abelian group that satisfies nD=D for all natural n. The theorem states that any divisible…

In this note, we prove that $D_8\times C_2^{n-3}$ is the non-elementary abelian $2$-group of order $2^n$, $n\geq 3$, whose number of subgroups of possible orders is maximal. This solves a conjecture by Haipeng Qu [7]. A formula for counting…

In this article, we study the derivations of group algebras of some important groups, namely, dihedral ($D_{2n}$), Dicyclic ($T_{4n}$) and Semi-dihedral ($SD_{8n}$). First, we explicitly classify all inner derivations of a group algebra…

We prove that the near hexagon $Q(5,2) \times \mathbb{L}_3$ has a non-abelian representation in the extra-special 2-group $2^{1+12}_+$ and that the near hexagon $Q(5,2) \otimes Q(5,2)$ has a non-abelian representation in the extra-special…

We explicitly determine all CI-groups with respect to ternary relational structures that have the form $C \times D$, where $C$ is cyclic and $D$ is either a dicyclic group whose order is not divisible by $3$ or a dihedral group. Such groups…

We prove two existing conjectures which describe the geometrical McKay correspondence for a finite abelian G in SL3(C) such that C^3/G has a single isolated singularity. We do it by studying the relation between the derived category…

We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a…

The purpose of this note is to construct an example of a discrete non-abelian group $G$ and a subset $E$ of $G$, not contained in any abelian subgroup, that is a completely bounded $\Lambda (p)$ set for all $p<\infty ,$ but is neither a…

We find a sufficient condition to establish that certain abelian groups are not CI-groups with respect to ternary relational structures, and then show that the groups $\Z_3\times\Z_2^2$, $\Z_7\times\Z_2^3$, and $\Z_5\times\Z_2^4$ satisfy…

Let $G$ be a finite group and $D_{2n}$ be the dihedral group of $2n$ elements. For a positive integer $d$, let $\mathsf{s}_{d\mathbb{N}}(G)$ denote the smallest integer $\ell\in \mathbb{N}_0\cup \{+\infty\}$ such that every sequence $S$…

Motivated by a connection between semi-regular relative difference sets and mutually unbiased bases, we study relative difference sets with parameters $(m,n,m,m/n)$ in groups of non-prime-power orders. Let $p$ be an odd prime. We prove that…

In this paper, we study the structure of the permutability graphs of subgroups, and the permutability graphs of non-normal subgroups of the following groups: the dihedral groups $D_n$, the generalized quaternion groups $Q_n$, the…

Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that if L is a component of the (stable)…

We derive the discrete anomaly conditions for the binary tetrahedral group T' as well as the binary dihedral groups Q_2n. The ambiguities of embedding these finite groups into SU(2) and SU(3) lead to various possible definitions of the…

We prove that any left-ordered inp-minimal group is abelian, and we provide an example of a non-abelian left-ordered group of dp-rank 2.

A finite group $G$ is a "non-DCI group" if there exist subsets $S_1$ and $S_2$ of $G$, such that the associated Cayley digraphs $C\overrightarrow{ay}(G;S_1)$ and $C\overrightarrow{ay}(G;S_2)$ are isomorphic, but no automorphism of $G$…

We build two non-abelian CSA-groups in which maximal abelian subgroups are conjugate and divisible.

In this paper we explicitly determine all indicators for groups isomorphic to the semidirect product of two cyclic groups by an automorphism of prime order, as well as the generalized quaternion groups. We then compute the indicators for…