Related papers: Les groupes de triangles $(2,p,q)$ sont d\'etermin…
Given a spectral triple of compact type with a real structure in the sense of [Dabrowski L., J. Geom. Phys. 56 (2006), 86-107] (which is a modification of Connes' original definition to accommodate examples coming from quantum group theory)…
Generalizing the involution length of the complex hyperbolic plane, we obtain that the $\alpha$-length of $\mathrm{PU}(2,1)$ is $4$, that is, every element of $\mathrm{PU}(2,1)$ can be decomposed as the product of at most $4$ special…
In this paper we determine the full character table of a certain split extension $H_1(q)\rtimes Sp(2,q)$ of the Heisenberg group $H_1$ by the odd-characteristic symplectic group $Sp(2,q)$.
Let $G$ denote the projective special linear group $\text{PSL}(2,q)$, for a prime power $q$. It is shown that a finite 2-subgroup of the group $V(\mathbb{Z}G)$ of augmentation 1 units in the integral group ring $\mathbb{Z}G$ of $G$ is…
Trianguline representations are a certain class of p-adic representations of Gal(Qp^alg/Qp) like the crystalline, semistable and de Rham representations of Fontaine. Their definition involves the theory of (phi,Gamma)-modules. In this…
We provide upper bounds on the $L(p,q)$-labeling number of graphs which have interval (or circular-arc) representations via simple greedy algorithms. We prove that there exists an $L(p,q)$-labeling with span at most…
In this short note we determine the set $\Phi^\infty(7)$ of Abelian groups that appear as torsion groups of infinitely many elliptic curves (up to $\overline \mathbb Q$-isomorphism) over number fields of degree 7.
The group $PGL(2,q)$ acts $3$-transitively on the projective line $GF(q) \cup \{\infty\}$. Thus, an orbit of its action on the $k$-subsets of the projective line is the block set of a $3$-$(q+1,k,\lambda)$ design. We find the parameters of…
Recent examples of periodic bifurcations in descendant trees of finite p-groups with p in {2,3} are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p-class group of type (2,2,2), resp. (3,3),…
When G is a finite abelian group, we define G-spans of groupoids and their associated matrices with entries in the group ring QG and show that composition of spans corresponds to multiplication of matrices.
In this article we combinatorially describe the triangles that are present in two types of line arrangements, those which have global cyclicity and those which are infinity type line arrangements. A combinatorial nomenclature has been…
The pineapple graph $K_p^q$ is obtained by appending $q$ pendant edges to a vertex of a complete graph $K_{p}$ ($q\geq 1,\ p\geq 3$). Zhang and Zhang ["Some graphs determined by their spectra", Linear Algebra and its Applications, 431…
We find exact and asymptotic formulas for the number of pairs $(p,q)$ of $N$-cycles such that the all cycles of the product $p\cdot q$ have lengths from a given integer set. We then apply these results to prove a surprisingly high lower…
We classify perimeter dominant triangles whose side lengths are in $\sqrt3\mathbb N$ and whose area is in $\frac{\sqrt3}4\mathbb N$. There is one exceptional example, which is equilateral, and three infinite families determined by certain…
Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially $q$-analogues, have useful interpretations related to actions and representations of the cyclic group. We propose a definition of sieving for an…
In this paper, we investigate finite solvable tidy groups. We classify the tidy $\{ p, q \}$-groups. Combining this with a previous result, we are able to characterize the finite tidy solvable groups. Using this characterization, we bound…
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
Two finite groups are said to be isospectral if they have the same sets of element orders. This paper completes the description of finite groups that are isospectral to finite simple groups with disconnected prime graph.
We prove that an algebraic group over a field $k$is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a…
We show that the Grothendieck-Teichm\"uller group of $PSL(2, q)$, or more precisely the group $GT_1(PSL(2, q))$ as previously defined by the author, is the product of an elementary abelian 2-group and several copies of the dihedral group of…