1,596 research outputs found
Restauri nel nord Sardegna. Temi e cantieri di restauro architettonico nell’attività della Soprintendenza BeAP di Sassari e Nuoro
No full textThe Möbius function of PSU(3, 22n)
No full textLet G be the simple group PSU(3, 22n), n > 0. For any subgroup H of G, we compute the Möbius function μL(H, G) of H in the subgroup lattice L of G, and the Möbius function μL ̄ ([H], [G]) of [H] in the poset L ̄ of conjugacy classes of subgroups of G. For any prime p, we provide the Euler characteristic of the order complex of the poset of non-trivial p-subgroups of G
On the spectrum of genera of quotients of the Hermitian curve
No full textWe investigate the genera of quotient curves Hq∕G of the Fq2 -maximal Hermitian curve Hq, where G is contained in the maximal subgroup Mq ≤ Aut (Hq) fixing a pole-polar pair (P,l) with respect to the unitary polarity associated with Hq. To this aim, a geometric and group-theoretical description of Mq is given. The genera of some other quotients Hq∕G with G≰Mq are also computed. In this way we obtain new values in the spectrum of genera of Fq2 -maximal curves. The complete list of genera g>1 of quotients of Hq is given for q≤29, as well as the genera g of quotients of Hq with g>q2q+30/32 for any q. As a direct application, we exhibit examples of Fq2 -maximal curves which are not Galois covered by Hq when q is not a cube. Finally, a plane model for Hq∕G is obtained when G is cyclic of order p⋅d, with d a divisor of q+1
Quotients of the Hermitian curve from subgroups of PGU(3,q) without fixed points or triangles
No full textIn this paper, we deal with the problem of classifying the genera of quotient curves Hq/G, where Hq is the Fq2 -maximal Hermitian curve and G is an automorphism group of Hq. The groups G considered in the literature fix either a point or a triangle in the plane PG(2, q6). In this paper, we give a complete list of genera of quotients Hq /G, when G ≤ Aut(Hq) ∼= PGU(3,q) does not leave invariant any point or triangle in the plane. Also, the classification of subgroups G of PGU(3,q) satisfying this property is given up to isomorphism
On two Möbius functions for a finite non-solvable group
No full textLet G be a finite group, μ be the Möbius function on the subgroup lattice of G, and λ be the Möbius function on the poset of conjugacy classes of subgroups of G. It was proved by Pahlings that, whenever G is solvable, the property (Formula presented.) holds for any subgroup H of G. It is known that this property does not hold in general, the Mathieu group M 12 being a counterexample. In this paper we investigate the relation between μ and λ for some classes of non-solvable groups, among them, the minimal non-solvable groups. We also provide several examples of groups not satisfying the property
Generalized Artin–Mumford curves over finite fields
No full textLet Fq be the finite field of order q=ph with p>2 prime and h>1, and let Fq ̄ be a subfield of Fq. From any two q ̄-linearized polynomials L1,L2∈F ̅q[T] of degree q, we construct an ordinary curve X(Ljavax.xml.bind.JAXBElement@3de21171,Ljavax.xml.bind.JAXBElement@44e73174) of genus g=(q−1)2 which is a generalized Artin–Schreier cover of the projective line P1. The automorphism group of X(Ljavax.xml.bind.JAXBElement@265fda03,Ljavax.xml.bind.JAXBElement@5ee20ea3) over the algebraic closure F ̅q of Fq contains a semidirect product Σ⋊Γ of an elementary abelian p-group Σ of order q2 by a cyclic group Γ of order q ̄−1. We show that for L1≠L2, Σ⋊Γ is the full automorphism group Aut(X(Ljavax.xml.bind.JAXBElement@4b2f1fff,Ljavax.xml.bind.JAXBElement@2ddc4e9)) over F ̅q; for L1=L2 there exists an extra involution and Aut(X(Ljavax.xml.bind.JAXBElement@2daa9e77,Ljavax.xml.bind.JAXBElement@1c89ae0d))=Σ⋊Δ with a dihedral group Δ of order 2(q ̄−1) containing Γ. Two different choices of the pair L1,L2 may produce birationally isomorphic curves, even for L1=L2. We prove that any curve of genus (q−1)2 whose F ̅q-automorphism group contains an elementary abelian subgroup of order q2 is birationally equivalent to X(Ljavax.xml.bind.JAXBElement@1301e61e,Ljavax.xml.bind.JAXBElement@61aac551) for some separable q ̄-linearized polynomials L1,L2 of degree q. We produce an analogous characterization in the special case L1=L2. This extends a result on the Artin–Mumford curves, due to Arakelian and Korchmáros [1]
On permutation trinomials of type x2ps+r+xps+r+λxr
No full textWe determine all permutation trinomials of type x(2ps+r) + x(ps+r) + lambda x(r) over the finite field F-pt when (2p(s) + r)(4) < p(t). This partially extends a previous result by Bhattacharya and Sarkar in the case p = 2, r = 1. (C) 2017 Elsevier Inc. All rights reserved
The Mobius function of PSL (3, 2 p) for any prime p
No full textLet G be the simple group PSL(3, 2p), where p is a prime number. For any subgroup H of G, we compute the Mobius function μ(H) of H in the subgroup lattice of G. To this aim, we describe the intersections of maximal subgroups of G. We point out some connections of the Mobius function with other combinatorial objects, and, in this context, we compute the reduced Euler characteristic of the order complex of the subposet of r-subgroups of PGL(3,q), for any prime r and any prime power q
COPRIME COMMUTATORS in the SUZUKI GROUPS
No full textIn this note we show that every element of a simple Suzuki group is a commutator of elements of coprime orders
On the classification problem for the genera of quotients of the Hermitian curve
No full textIn this article, we characterize the genera of those quotient curves H q /G of the F q 2-maximal Hermitian curve H q for which either G is contained in the maximal subgroup M 1 of (H q ) fixing a self-polar triangle, or q is even and G is contained in the maximal subgroup M 2 of (H q ) fixing a pole-polar pair (P,l) with respect to the unitary polarity associated to H q (F q 2) In this way, several new values for the genus of a maximal curve over a finite field are obtained. Our results leave just two open cases to provide the complete list of genera of Galois subcovers of the Hermitian curve; namely, the open cases in [4] when G fixes a point P∈H q (F q 2) and q is even, and the open cases in [33] when G≤M 2 and q is odd
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