Ricerche di Matematica最新文献

In this article, we study some properties of Ricci solitons with quarter-symmetric connection, when the soliton vector field is torse-forming. We also study some applications of quarter-symmetric connection on Riemannian submanifolds. This paper extends the results obtained by Ozgur (Filomat, 35:11(2021), 3635-3641) to the setting of quarter-symmetric connections.

Let G be a group. If the set ({mathcal {A}}(G)=lbrace alpha in {textit{Aut}}(G): xalpha (x)=alpha (x)x; textit{for all}; xin Grbrace ) forms a subgroup of ({textit{Aut}}(G)), then G is called ({mathcal {A}})-group. In this paper, we prove that a metacyclic group is an ({mathcal {A}})-group. Also, we show that, for any positive integer n and any prime number p, there exists a finite ({mathcal {A}}) p-group of nilpotency class n. Since there exist finite non ({mathcal {A}}) p-groups with (vert G/G^{prime }vert = p^{4}), we find suitable conditions implying that a finite p-group with (vert G/G^{prime }vert le p^{3}) is an ({mathcal {A}})-group. Using these results, we show that there exists a finite ({mathcal {A}}) p-group G of order (p^{n}) for all (nge 4) such that ({mathcal {A}}(G)) is equal to the central automorphisms group of G. Finally, we use semidirect product and wreath product of groups to obtain suitable examples.

Let (mathbb {P}) be the set of all prime numbers, I be a set and (sigma = lbrace sigma _i mid i in I rbrace ) be a partition of (mathbb {P}). A finite group is said to be (sigma )-primary if it is a (sigma _i)-group for some (i in I), and we say that a finite group is (sigma )-solvable if all its chief factors are (sigma )-primary. A subgroup H of a finite group G is said to be (sigma )-subnormal in G if there is a chain (H = H_0 le H_1 le dots le H_n = G) of subgroups of G such that (H_{i-1}) is normal in (H_i) or (H_i/(H_{i-1})_{H_i}) is (sigma )-primary for all (1 le i le n). Given subgroups H and A of a (sigma )-solvable finite group G, we prove two criteria for H to be (sigma )-subnormal in (langle H, A rangle ). Our criteria extend classical subnormality criteria of Fumagalli [5], which themselves generalize a classical subnormality criterion of Wielandt [13].

In the present work, we attempt to identify classes of bivariate distributions of random vector (X, Y) in which ageing concepts like increasing hazard rates, decreasing mean residual life, etc. can be inferred from univariate ageing properties of a random variable Z whose distribution specifies the dependence structure between the components of (X, Y). It is shown that a family of bivariate exponential distributions and those obtained by monotone transformations from them, and the time-transformed exponential models satisfy this property. The bivariate distributions considered here are exchangeable and the notions of ageing are interpreted in a Bayesian sense.

We show that, for any q, the pointset covered by the conic planes of a quadric Veronesean of (textrm{PG}(3,q)) is a two character set with respect to hyperplanes of (textrm{PG}(9,q)).

In this paper we investigate hyperplanes of the point-line geometry (A_{n,{1,n}}(mathbb {F})) of point-hyerplane flags of the projective geometry (textrm{PG}(n,mathbb {F})). Renouncing a complete classification, which is not yet within our reach, we describe the hyperplanes which arise from the natural embedding of (A_{n,{1,n}}(mathbb {F})), that is the embedding which yields the adjoint representation of (textrm{SL}(n+1,mathbb {F})). By exploiting properties of a particular sub-class of these hyerplanes, namely the singular hyperplanes, we shall prove that all hyperplanes of (A_{n,{1,n}}(mathbb {F})) are maximal subspaces of (A_{n,{1,n}}(mathbb {F})). Hyperplanes of (A_{n,{1,n}}(mathbb {F})) can also be contructed starting from suitable line-spreads of (textrm{PG}(n,mathbb {F})) (provided that (textrm{PG}(n,mathbb {F})) admits line-spreads, of course). Explicitly, let (mathfrak {S}) be a composition line-spread of (textrm{PG}(n,mathbb {F})) such that every hyperplane of (textrm{PG}(n,mathbb {F})) contains a sub-hyperplane of (textrm{PG}(n,mathbb {F})) spanned by lines of (mathfrak {S}). Then the set of points (p, H) of (A_{n,{1,n}}(mathbb {F})) such that H contains the member of (mathfrak {S}) through p is a hyperplane of (A_{n,{1,n}}(mathbb {F})). We call these hyperplanes hyperplanes of spread type. Many but not all of them arise from the natural embedding.

Let G be a finite group. A subgroup H of G is called Hall normally embedded in G if H is a Hall subgroup of the normal closure (H^G). In this paper, we fix a subgroup D of Sylow p-subgroup P of G with (1<|D|<|O_p(G)|) and study the structure of G under the assumption that all subgroups H of P with order (|H|=|D|) are Hall normally embedded in G.

We prove a conjecture on the Chow ring of characteristic classes for the special Clifford groups. This conjecture was the only obstacle for obtaining an algorithm computing the maximal indexes of twisted spin grassmannians.

Let (p) be a fixed prime, (a) and (n) are positive integers such that ((p,n) = 1). It is shown that if (G) is a finite group such that for every prime (q) the set of the conjugacy class sizes of all ({ p,q} -) elements of (G) is (left{ {1,p^{a} {,}n,p^{a} n} right}), and there is a (p -) element in (G) whose conjugacy class has size (p^{a}), then (G) is nilpotent and (n) is a prime power.

The non-equilibrium phenomena that characterize the dynamics of an oscillating bubble in a liquid are generally very complex. In this work we study the effects produced by the presence of a gas mixture in which the temperatures of each species are taken into account. Acceleration waves are used to test the stabilizing effects of the model and verify the possibility of shock formation within the bubble. It is shown that the diffusion associated with the presence of multiple temperatures cannot be neglected when describing what happens inside the bubble, even in the sonoluminescence regime.