Acta Mathematica Hungarica最新文献

We study some families of finite groups having inner class-preservingautomorphisms. In particular, let G be a finite group and S be asemidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is nota homomorphic image of G and (Z(S) < Z(G)) or G is nilpotent-by-nilpotent, wehave that all the Coleman automorphisms of G are inner. As a consequence, thesegroups satisfy the normalizer problem.

Many real-world networks exhibit the phenomenon of edge clustering,which is typically measured by the average clustering coefficient. Recently,an alternative measure, the average closure coefficient, is proposed to quantify local clustering. It is shown that the average closure coefficient possesses a number of useful properties and can capture complementary information missed by the classical average clustering coefficient. In this paper, we study the asymptotic distribution of the average closure coefficient of a heterogeneous Erdős–Rényi random graph. We prove that the standardized average closure coefficient converges in distribution to the standard normal distribution. In the Erdős–Rényi random graph,the variance of the average closure coefficient exhibits the same phase transition phenomenon as the average clustering coefficient.

We characterize algebraic integers which are differences of twoPisot numbers. Each such number (alpha) must be real and its conjugates over (mathbb{Q}) mustall lie in the union of the disc (|z|<2) and the strip (|Im(z)|<1). In particular, weprove that every real algebraic integer (alpha) whose conjugates over (mathbb{Q}), except possiblyfor (alpha) itself, all lie in the disc (|z|<2) can always be written as a difference oftwo Pisot numbers. We also show that a real quadratic algebraic integer (alpha) withconjugate (alpha') over (mathbb{Q}) is always expressible as a difference of two Pisot numbers exceptfor the cases (alpha<alpha'<-2) or (2<alpha'<alpha) when (alpha) cannot be expressed in thatform. A similar complete characterization of all algebraic integers (alpha) expressibleas a difference of two Pisot numbers in terms of the location of their conjugatesis given in the case when the degree (d) of (alpha) is a prime number.

We study the index (i(K)) of any septic number field (K) generatedby a root of an irreducible trinomial of type (F(x)=x^7+ax^2+b in mathbb{Z}[x]). We showthat the unique prime which can divide (i(K)) is (2). Moreover, we give necessaryand sufficient conditions on (a) and (b) so that (2) is a common index divisor of (K).Further, we show that (i(K)=2) whenever (2) divides (i(K)). In this way, we answercompletely Problem (6) and Problem (22) of Narkiewicz [34] for these families of number fields. As an application of our results, if (2) divides (i(K)), then the ring(mathcal{O}_K) of integers of (K) has no power integral basis. We illustrate our results bygiving some numerical examples.

Using square bridge position, Akbulut-Ozbagci and later Arikan gave algorithms both of which construct an explicit compatible open book decomposition on a closed contact 3-manifold which results from a contact ((pm 1))-surgery on a Legendrian link in the standard contact 3-sphere. In this article, we introduce the “generalized square bridge position” for a Legendrian link in the standard contact 5-sphere and partially generalize this result to the dimension five via an algorithm which constructs relative open book decompositions on relative contact pairs.

We introduce several martingale Orlicz-Hardy spaces with continuoustime. By use of the atomic decomposition, we establish some martingaleinequalities and characterize the dualities of these spaces.

Let ((t(m))_{m ge0}) be Thue-Morse sequence and (b>2) be an integer.In this paper, we prove that the real numbers (1), (sum_{m=0}^infty {frac{t(m^2)}{{b}^{m+1}}}) and (sum_{m=0}^infty {frac{t(m^3)}{{b}^{m+1}}}) arelinearly independent over (mathbb{Q}).

Fix an integer (kappage 2). Let (Pge 2) be a prime, and (F) be thesymmetric-square lift of a Hecke newform (fin mathcal{S}^ {ast} _kappa(P)). We study the exponential sum

by implementing an average over a family in such a way to investigate the bestpossible magnitude of the level aspect bound for (mathscr{L}_F(alpha)). We prove a uniformbound with respect to any (alpha in mathbb{R}) and the level parameter (P), and present thatthere exist certain forms with fairly strong oscillations in (mathscr{L}_F(alpha)), if the associatedlevel of (f) is allowed to vary. As applications, we consider the shifted convolutionsums for ( mathrm{GL} (3)times mathrm{GL} (d)), for any (dge 2), in a family as well as theWaring-Goldbachproblem associated to Fourier coefficients of ( mathrm{SL} (3,mathbb{Z}))-Maa(beta) forms.

We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting behaviour of slender groups. Secondly, we remove the condition of being abelian and consider nilpotent periodic locally compact p-groups (p prime), reducing the computations to the case of Sylow p-subgroups. Finally, we investigate locally compact Heisenberg p-groups (mathbb{H}_n (mathbb{Q}_ p )) on the field (mathbb{Q}_ p ) of the p-adic rationals with n arbitrary positive integer.