1,720,999 research outputs found
Module braces: relations between the additive and the multiplicative groups
No full textIn this paper, we define a class of braces that we call module braces or R-braces, which are braces for which the additive group has also a module structure over a ring R, and for which the values of the gamma functions are automorphisms of R-modules. This class of braces has already been considered in the literature in the case where the ring R is a field; we generalise the definition to any ring R, reinterpreting it in terms of the so-called gamma function associated with the brace, and prove that this class of braces enjoys all the natural properties one can require. We exhibit explicit example of R-braces, and we study the splitting of a module braces in relation to the splitting of the ring R, generalising thereby Byott's result on the splitting of a brace with nilpotent multiplicative group as a sum of its Sylow subgroups. The core of the paper is in the last two sections, in which, using methods from commutative algebra and number theory, we study the relations between the additive and the multiplicative groups of an R-brace showing that if a certain decomposition of the additive group is small (in some sense which depends on R), then the additive and the multiplicative groups have the same number of elements of each order. In some cases, this result considerably broadens the range of applications of the results already known on this issue
Hopf-Galois structures on extensions of degree p2q and skew braces of order p2q: The cyclic Sylow p-subgroup case
Full text linkLet p,q be distinct primes, with p>2. We classify the Hopf-Galois structures on Galois extensions of degree p2q, such that the Sylow p-subgroups of the Galois group are cyclic. This we do, according to Greither and Pareigis, and Byott, by classifying the regular subgroups of the holomorphs of the groups (G,⋅) of order p2q, in the case when the Sylow p-subgroups of G are cyclic. This is equivalent to classifying the skew braces (G,⋅,∘). Furthermore, we prove that if G and Γ are groups of order p2q with non-isomorphic Sylow p-subgroups, then there are no regular subgroups of the holomorph of G which are isomorphic to Γ. Equivalently, a Galois extension with Galois group Γ has no Hopf-Galois structures of type G. Our method relies on the alternate brace operation ∘ on G, which we use mainly indirectly, that is, in terms of the functions γ:G→Aut(G) defined by g↦(x↦(x∘g)⋅g−1). These functions are in one-to-one correspondence with the regular subgroups of the holomorph of G, and are characterised by the functional equation γ(gγ(h)⋅h)=γ(g)γ(h), for g,h∈G. We develop methods to deal with these functions, with the aim of making their enumeration easier, and more conceptual
How far is an extension of p-adic fields from having a normal integral basis?
No full textLet L/K be a finite Galois extension of p-adic fields with group G. It is well-known that OL contains a free OK[G]-submodule of finite index. We study the minimal index of such a free submodule, and determine it exactly in several cases, including for any cyclic extension of degree p of p-adic fields
THE AUTOMORPHISM GROUPS OF GROUPS OF ORDER p(2)q
No full textWe record for reference a detailed description of the automorphism groups of the groups of order p(2)q, where p and q are distinct primes
On Fuchs’ problem for finitely generated abelian groups: The small torsion case
No full textAclassical problem, raised by Fuchs in 1960, asks to classify
the abelian groupswhich are groups of units of some
rings. In this paper, we consider the case of finitely generated
abelian groups, solving Fuchs’ problem for such
groups with the additional assumption that the torsion
subgroups are small, for a suitable notion of small related
to the Prüfer rank. As a concrete instance, we classify for
each n ⩾ 2 the realisable groups of the form Z∕nZ × Zr.
Our tools require an investigation of the adjoint group of
suitable radical rings of odd prime power order appearing
in the picture, giving conditions under which the
additive and adjoint groups are isomorphic. In the last
section, we also deal with some groups of order a power
of 2, proving that the groups of the form Z∕4Z × Z∕2uZ
are realisable if and only if 0 ⩽ u ⩽ 3 or 2u + 1is a Fermat
prime
Upper ramification jumps in abelian extensions of exponent p
Full text linkIn this paper we present a classification of the possible upper ramification jumps for an elementary abelian -extension of a -adic field.
The fundamental step for the proof of the main result is the computation
of the ramification filtration for the maximal elementary abelian -extension of the base field . This result generalizes
\cite[Lemma 9, p. 286]{Del_Corso_Dvornicich_2007}, where the same result is proved under the assumption
that contains a primitive -th root of unity. To deal with this general case we use class field theory and the explicit relations
between the normic group of an extension and its ramification jumps, and we obtain necessary and sufficient conditions for
the upper ramification jumps of an elementary abelian -extension of
Free circulating interleukin-18 is increased in Schnitzler syndrome: a new autoinflammatory disease?
No full textSchnitzler syndrome is a rare disease characterised by chronic urticaria and arthralgia. The recent evidence that the IL-1 receptor antagonist IL-1Ra could induce rapid and complete remission of Schnitzler symptoms has pointed to IL-1 as a major pathological factor in this disease. To examine the possibility that Schnitzler syndrome may be considered to be an autoinflammatory disease, in this study we measured the serum levels of IL-18, another cytokine of the IL-1 family that is cleaved by caspase-1, in two recently diagnosed Schnitzler patients before and after treatment with IL-1Ra. In parallel, mRNA expression of IL-1 family cytokines and caspase-1 were assessed in isolated blood monocytes. Treatment with IL-1Ra significantly inhibited IL-1beta gene expression, indicating that IL-1beta activity in Schnitzler syndrome is central to IL-1beta gene upregulation in a type of auto-amplification loop. While no IL-1beta was detected in serum, free circulating IL-18 was increased in patients with Schnitzler syndrome, despite low IL-18 gene expression in monocytes. This suggests constitutive activation of the IL-1beta/IL-18-producing inflammasome, and supports the hypothesis that Schnitzler's syndrome is a new autoinflammatory disease
Hopf-Galois structures on extensions of degree and skew braces of order : the elementary abelian Sylow -subgroup case
Full text linkLet be distinct primes, with . In a previous paper we
classified the Hopf-Galois structures on Galois extensions of degree ,
when the Sylow -subgroups of the Galois group are cyclic. This is equivalent
to classifying the skew braces of order , for which the Sylow
-subgroups of the multiplicative group is cyclic. In this paper we complete
the classification by dealing with the case when the Sylow -subgroups of the
Galois group are elementary abelian.
According to Greither and Pareigis, and Byott, we will do this by classifying
the regular subgroups of the holomorphs of the groups of order
, in the case when the Sylow -subgroups of are elementary
abelian.
We rely on the use of certain gamma functions . These functions are in one-to-one correspondence with
the regular subgroups of the holomorph of , and are characterised by the
functional equation , for
. We develop methods to deal with these functions, with the aim of
making their enumeration easier and more conceptual.Comment: 95 page
Hypersensitivity reactions during treatment with biological agents
No full textThe recent development of biological agents, namely, anti-tumour necrosis factor alpha (TNF-α) agents (infliximab, adalimumab and etanercept), anti-CD20 monoclonal antibody (rituximab) and anti-interleukin 6 receptor (IL-6R) monoclonal antibody (tocilizumab), represents a major breakthrough for the treatment of immune-mediated disorders. Given their structural and functional differences, distinct safety profiles can be expected for each of these agents. Evidence in the literature indicates that patients treated with anti-TNF-α agents and tocilizumab are at increased risk for bacterial infections. However, an increased therapeutic use of these biological agents has disclosed other side-effects, including immediate hypersensitivity reactions, such as anaphylaxis and urticaria.
Both under-diagnosis and over-diagnosis of hypersensitivity reactions to biological agents are potential problems. Thus, it is important to identify these reactions and to adopt the right approach to manage them.
This article reviews the general aspects of adverse events during biologic treatment, focusing on IgE-mediated hypersensitivity reactions to anti-TNF-α agents, rituximab and tocilizumab, and on the tools for the diagnosis of these life-threatening reactions
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