Related papers: On prime order automorphisms of generalized quadra…

For $k,s\geq2$, the $s$-stable Kneser graphs are the graphs with vertex set the $k$-subsets $S$ of $\{1,\ldots,n\}$ such that the circular distance between any two elements in $S$ is at least $s$ and two vertices are adjacent if and only if…

Let $G(X,Y)$ be a connected, non-complete bipartite graph with $|X|\leq |Y|$. An independent set $A$ of $G(X,Y)$ is said to be trivial if $A\subseteq X$ or $A\subseteq Y$. Otherwise, $A$ is nontrivial. By $\alpha(X,Y)$ we denote the size of…

In this paper we investigate when the generic member of a family of K3 surfaces admitting a non--symplectic automorphism of finite order admits also a symplectic automorphism of the same order. We give a complete answer to this question if…

We prove the following theorem: let $A$ be a UCT Kirchberg algebra, and let $\alpha$ be a prime-order automorphism of $K_*(A)$, with $\alpha([1_A])=[1_A]$ in case $A$ is unital. Then $\alpha$ is induced from an automorphism of $A$ having…

Induced by three gluons symmetry, Mandelstam variables $s$, $t$, $u$ symmetric expressions are widely involved in collider physics, especially in heavy quarkonium physics. In this work we study general form of $s$, $t$, $u$ symmetric…

In this paper we study the existence of at least one non-inner automorphism of order p in a finite normally constrained p-group when p is an odd prime.

A {\em generalized hyperfocused arc} $\mathcal H $ in $PG(2,q)$ is an arc of size $k$ with the property that the $k(k-1)/2$ secants can be blocked by a set of $k-1$ points not belonging to the arc. We show that if $q$ is a prime and…

In this paper, we consider the possible types of regular maps of order $2^n$, where the order of a regular map is the order of automorphism group of the map. For $n \le 11$, M. Conder classified all regular maps of order $2^n$. It is easy…

In this paper, generalized Cayley graphs are studied. It is proved that every generalized Cayley graph of order 2p is a Cayley graph, where p is a prime. Special attention is given to generalized Cayley graphs on Abelian groups. It is…

A Mumford curve of genus g (>1) over a non-archimedean valued field k of positive characteristic has at most max{12(g-1), 2 g^(1/2) (g^(1/2)+1)^2} automorphisms. This bound is sharp in the sense that there exist Mumford curves of arbitrary…

Fix distinct primes $p$ and $q$ and let $E$ be an elliptic curve defined over a number field $K$. The $(p,q)$-entanglement type of $E$ over $K$ is the isomorphism class of the group $\operatorname{Gal}(K(E[p])\cap K(E[q])/K)$. The size of…

Suppose we have a finite thick generalised quadrangle whose automorphism group $G$ acts primitively on both the set of points and the set of lines. Then $G$ must be almost simple. In this paper, we show that $\operatorname{soc}(G)$ cannot…

Groups of order $4$ are isomorphic to either $\mathbb{Z}/4\mathbb{Z}$ or $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$. We give certain sufficient conditions permitting to specify the structure of class groups of order $4$ in the…

In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…

We prove that random-cluster models with q larger than 1 on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter p_c below which the model exhibits exponential decay and above which there…

We prove that, on average, elliptic curves over Q have finitely many primes p for which they possess a p-adic point of order p. We include a discussion of applications to companion forms and the deformation theory of Galois representations.

Let $q>2$ be a prime power and $f={\tt x}^{q-2}+t{\tt x}^{q^2-q-1}$, where $t\in\Bbb F_q^*$. It was recently conjectured that $f$ is a permutation polynomial of $\Bbb F_{q^2}$ if and only if one of the following holds: (i) $t=1$, $q\equiv…

In this article, we study some cyclic $(r,s)$ curves $X$ given by $y^r =x^s + \lambda_{1} x^{s-1} +...+ \lambda_{s-1} x + \lambda_s$. We give an expression for the prime form $\cE(P,Q)$, where $(P, Q \in X)$, in terms of the sigma function…

A graph $\Ga=(V,E)$ is called a Cayley graph of some group $T$ if the automorphism group $\Aut(\Ga)$ contains a subgroup $T$ which acts on regularly on $V$. If the subgroup $T$ is normal in $\Aut(\Ga)$ then $\Ga$ is called a normal Cayley…

For a prime $p$, let $F_q$ be the finite field of order $q= p^d$. This paper presents the study on skew generalized quasi-cyclic (SGQC) codes of length $n$ over the non-chain ring $F_q+vF_q$ where $v^2=v$ and $\theta_t$ is the Galois…