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1.
Let p be an odd prime number. We describe the Whitehead group of all extra-special and almost extra-special p-groups. For this we compute, for any finite p-group P, the subgroup of , in terms of a genetic basis of P. We also introduce a deflation map , for a normal subgroup N of P, and show that it is always surjective. Along the way, we give a new proof of the result describing the structure of , when P is an elementary abelian p-group. 相似文献
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Charles Almeida Aline V. Andrade Rosa M. Miró-Roig 《Journal of Pure and Applied Algebra》2019,223(4):1817-1831
Let be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators of lies in the interval . In this paper, we prove that for and , the integer values in cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems of forms of degree d with or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for , and there exists a minimal monomial Togliatti system of forms of degree d with . 相似文献
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Sanming Zhou 《Journal of Pure and Applied Algebra》2019,223(3):931-947
We study two families of cyclotomic graphs and perfect codes in them. They are Cayley graphs on the additive group of , with connection sets and , respectively, where () is an mth primitive root of unity, A a nonzero ideal of , and ? Euler's totient function. We call them the mth cyclotomic graph and the second kind mth cyclotomic graph, and denote them by and , respectively. We give a necessary and sufficient condition for to be a perfect t-code in and a necessary condition for to be such a code in , where is an integer and D an ideal of containing A. In the case when , is known as an Eisenstein–Jacobi and Gaussian networks, respectively, and we obtain necessary conditions for to be a perfect t-code in , where with β dividing α. In the literature such conditions are known to be sufficient when and under an additional condition. We give a classification of all first kind Frobenius circulants of valency 2p and prove that they are all pth cyclotomic graphs, where p is an odd prime. Such graphs belong to a large family of Cayley graphs that are efficient for routing and gossiping. 相似文献
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Jacques Darné 《Journal of Pure and Applied Algebra》2019,223(12):5484-5525
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We construct invariant polynomials on truncated multicurrent algebras, which are Lie algebras of the form , where is a finite-dimensional Lie algebra over a field of characteristic zero, and I is a finite-codimensional ideal of generated by monomials. In particular, when is semisimple and is algebraically closed, we construct a set of algebraically independent generators for the algebra of invariant polynomials. In addition, we describe a transversal slice to the space of regular orbits in . As an application of our main result, we show that the center of the universal enveloping algebra of acts trivially on all irreducible finite-dimensional representations provided I has codimension at least two. 相似文献
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We study G-vertex-primitive and -arc-transitive digraphs for almost simple groups G with socle . We prove that for such digraphs, which provides the first step in determining an upper bound on s for all the vertex-primitive s-arc-transitive digraphs. 相似文献
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Mi Hee Park 《Journal of Pure and Applied Algebra》2019,223(9):3980-3988
There are many Noetherian-like rings. Among them, we are interested in SFT-rings, piecewise Noetherian rings, and rings with Noetherian prime spectrum. Some of them are stable under polynomial extensions but none of them are stable under power series extensions. We give partial answers to some open questions related with stabilities of such rings. In particular, we show that any mixed extensions over a zero-dimensional SFT ring R are also SFT-rings, and that if R is an SFT-domain such that is integrally closed for each prime ideal P of R, then is an SFT-ring. We also give a direct proof that if R is an SFT Prüfer domain, then is an SFT-ring. Finally, we show that the power series extension over a Prüfer domain R is piecewise Noetherian if and only if R is Noetherian. 相似文献
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We define a ribbon category , depending on a parameter β, which encompasses Cautis, Kamnitzer and Morrison's spider category, and describes for the monoidal category of representations of generated by exterior powers of the vector representation and their duals. We identify this category with a direct limit of quotients of a dual idempotented quantum group , proving a mixed version of skew Howe duality in which exterior powers and their duals appear at the same time. We show that the category gives a unified natural setting for defining the colored link invariant (for ) and the colored HOMFLY-PT polynomial (for β generic). 相似文献
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Julia Semikina 《Journal of Pure and Applied Algebra》2019,223(10):4509-4523
I. Hambleton, L. Taylor and B. Williams conjectured a general formula in the spirit of H. Lenstra for the decomposition of for any finite group G and noetherian ring R. The conjectured decomposition was shown to hold for some large classes of finite groups. D. Webb and D. Yao discovered that the conjecture failed for the symmetric group , but remarked that it still might be reasonable to expect the HTW-decomposition for solvable groups. In this paper we show that the solvable group is also a counterexample to the conjectured HTW-decomposition. Nevertheless, we prove that for any finite group G the rank of does not exceed the rank of the expression in the HTW-decomposition. We also show that the HTW-decomposition predicts correct torsion for for any finite group G. Furthermore, we prove that for any degree other than the conjecture gives a correct prediction for the rank of . 相似文献
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Let C be a chain complex of finitely generated free modules over a commutative Laurent polynomial ring in s indeterminates. Given a group homomorphism we let denote the resulting induced complex over the Laurent polynomial ring in t indeterminates. We prove that the Betti number jump loci, that is, the sets of those homomorphisms p such that , have a surprisingly simple structure. We allow non-unital commutative rings of coefficients, and work with a notion of Betti numbers that generalises both the usual one for integral domains, and the analogous concept involving McCoy ranks in case of unital commutative rings. 相似文献
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Let FH be a supersolvable Frobenius group with kernel F and complement H. Suppose that a finite group G admits FH as a group of automorphisms in such a manner that and is nilpotent of class c. We show that G is nilpotent of -bounded class. 相似文献
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Katrina Barron Nathan Vander Werf Jinwei Yang 《Journal of Pure and Applied Algebra》2019,223(8):3295-3317
Motivated by the study of indecomposable, nonsimple modules for a vertex operator algebra V, we study the relationship between various types of V-modules and modules for the higher level Zhu algebras for V, denoted , for , first introduced by Dong, Li, and Mason in 1998. We resolve some issues that arise in a few theorems previously presented when these algebras were first introduced, and give examples illustrating the need for certain modifications of the statements of those theorems. We establish that whether or not is isomorphic to a direct summand of affects the types of indecomposable V-modules which can be constructed by inducing from an -module, and in particular whether there are V-modules induced from -modules that were not already induced by . We give some characterizations of the V-modules that can be constructed from such inducings, in particular as regards their singular vectors. To illustrate these results, we discuss two examples of : when V is the vertex operator algebra associated to either the Heisenberg algebra or the Virasoro algebra. For these two examples, we show how the structure of in relationship to determines what types of indecomposable V-modules can be induced from a module for the level zero versus level one Zhu algebras. We construct a family of indecomposable modules for the Virasoro vertex operator algebra that are logarithmic modules and are not highest weight modules. 相似文献
15.
Md. Ali Zinna 《Journal of Pure and Applied Algebra》2019,223(2):783-793
Let R be a commutative Noetherian ring of dimension two with and let . Let P be a projective A-module of rank 2. In this article, we prove that P is cancellative if is cancellative. 相似文献
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In this paper we consider the curves defined over and give a positive answer to a conjecture about a divisibility condition on L-polynomials of the curves . Our proof involves finding an exact formula for the number of -rational points on for all n, and uses a result we proved elsewhere about the number of rational points on supersingular curves. 相似文献
19.
Let be the finite field of order q. Let G be one of the three groups , or and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials such that for all cases except when and or . 相似文献