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Cristhian E. Hidber Miguel A. Xicoténcatl 《Journal of Pure and Applied Algebra》2018,222(6):1478-1488
The purpose of this article is to compute the mod 2 cohomology of , the mapping class group of the Klein bottle with q marked points. We provide a concrete construction of Eilenberg–MacLane spaces and fiber bundles , where denotes the configuration space of unordered q-tuples of distinct points in and is the classifying space of the group . Moreover, we show the mod 2 Serre spectral sequence of the bundle above collapses. 相似文献
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Let be a field of q elements, where q is a power of an odd prime p. The polynomial defined by has the property that where ρ is the quadratic character on . This univariate identity was applied to prove a recent theorem of N. Katz. We formulate and prove a bivariate extension, and give an application to quadratic residuacity. 相似文献
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Binzhou Xia 《Discrete Mathematics》2017,340(10):2469-2471
The covering radius of a subset of the symmetric group is the maximal Hamming distance of an element of from . This note determines the covering radii of the finite -dimensional projective general linear groups. It turns out that the covering radius of is if is even, and is if is odd. 相似文献
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In this paper, we consider the function field analogue of the Lehmer's totient problem. Let and be the Euler's totient function of over , where is a finite field with q elements. We prove that if and only if (i) is irreducible; or (ii) , is the product of any 2 non-associate irreducibles of degree 1; or (iii) , is the product of all irreducibles of degree 1, all irreducibles of degree 1 and 2, and the product of any 3 irreducibles one each of degree 1, 2 and 3. 相似文献
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Sunghyu Han Jon-Lark Kim Heisook Lee Yoonjin Lee 《Finite Fields and Their Applications》2012,18(3):613-633
There is a one-to-one correspondence between ?-quasi-cyclic codes over a finite field and linear codes over a ring . Using this correspondence, we prove that every ?-quasi-cyclic self-dual code of length m? over a finite field can be obtained by the building-up construction, provided that or , m is a prime p, and q is a primitive element of . We determine possible weight enumerators of a binary ?-quasi-cyclic self-dual code of length p? (with p a prime) in terms of divisibility by p. We improve the result of Bonnecaze et al. (2003) [3] by constructing new binary cubic (i.e., ?-quasi-cyclic codes of length 3?) optimal self-dual codes of lengths (Type I), 54 and 66. We also find quasi-cyclic optimal self-dual codes of lengths 40, 50, and 60. When , we obtain a new 8-quasi-cyclic self-dual code over and a new 6-quasi-cyclic self-dual code over . When , we find a new 4-quasi-cyclic self-dual code over and a new 6-quasi-cyclic self-dual code over . 相似文献
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Vladimir Shchigolev 《Journal of Algebra》2009,321(5):1453-1462
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Tathagata Basak 《Journal of Pure and Applied Algebra》2018,222(10):3036-3042
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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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In this paper, we present several necessary conditions for the reversed Dickson polynomial of the second kind to be a permutation of . In particular, we give explicit evaluation of the sum . 相似文献
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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献