Galois scaffolds and Galois module structure in extensions of characteristic p local fields of degree p2

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.A Galois scaffold, in a Galois extension of local fields with perfect residue fields, is an adaptation of the normal basis to the valuation of the extension field, and thus can be applied to answer questions of Galois module structure. Here we give a sufficient condition for a Galois scaffold to exist in fully ramified Galois extensions of degree p2 of characteristic p local fields. This condition becomes necessary when we restrict to p = 3. For extensions L/K of degree p2 that satisfy this condition, we determine the Galois module structure of the ring of integers by finding necessary and sufficient conditions for the ring of integers of L to be free over its associated order in K[Gal(L/K)]

A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordLet S/R be a finite extension of discrete valuation rings of characteristic p>0, and suppose that the corresponding extension L/K of fields of fractions is separable and is H-Galois for some K-Hopf algebra H. Let DS/R be the different of S/R. We show that if S/R is totally ramified and its degree n is a power of p, then any element ρ of L with vL(ρ)≡−vL(DS/R)−1(modn) generates L as an H-module. This criterion is best possible. These results generalise to the Hopf-Galois situation recent work of G. G. Elder for Galois extensions

Nilpotent and abelian Hopf-Galois structures on field extensions

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Let L/K be a finite Galois extension of fields with group Γ . When Γ is nilpotent, we show that the problem of enumerating all nilpotent Hopf–Galois structures on L/K can be reduced to the corresponding problem for the Sylow subgroups of Γ . We use this to enumerate all nilpotent (resp. abelian) Hopf–Galois structures on a cyclic extension of arbitrary finite degree. When Γ is abelian, we give conditions under which every abelian Hopf–Galois structure on L/K has type Γ . We also give a criterion on n such that every Hopf–Galois structure on a cyclic extension of degree n has cyclic type

SUARA PENDENGAR TENTANG LALU LINTAS (Studi Analisis Isi Suara Pendengar Tentang Lalu Lintas di Program Kelana Kota Radio Suara Surabaya Periode Bulan Februari 2013)

Hanti Kuspriyani, D0209038, SUARA PENDENGAR TENTANG LALU LINTAS (Studi Analisis Isi Suara Pendengar Tentang Lalu Lintas Di Program Kelana Kota Radio Suara Surabaya Periode Februari 2013), Skripsi (S-1), Program Studi Ilmu Komunikasi, Fakultas Ilmu Sosial dan Ilmu Politik, Universitas Sebelas Maret Surakarta, 2013. Menurut undang-undang nomor 22 tahun 2009, lalu lintas diartikan sebagai gerak kendaraan dan orang di ruang lalu lintas jalan. Sedangkan ruang lalu lintas didefinisikan sebagai prasarana yang diperuntukkan bagi gerak pindah kendaraan, orang, dan/atau barang yang berupa jalan dan fasilitas pendukung. Beberapa hal terkait lalu lintas yang menjadi pusat perhatian masyarakat meliputi kondisi lalu lintas, kecelakaan, fasilitas, pelanggaran, dan manajemen. Radio Suara Surabaya merupakan radio yang dijuluki sebagai radio “Lalu Lintas”. Hal ini terjadi karena sebanyak 48,93 % informasi interaktifnya merupakan informasi lalu lintas (sumber : Research and Development Suara Surabaya). Setiap harinya terdapat kurang lebih seribu pendengar yang bergabung untuk melaporkan informasi lalu lintas yang terjadi di sekitar mereka. Penelitian ini bermaksud untuk mengetahui bagaimana isi suara pendengar tentang lalu lintas di program Kelana Kota Radio Suara Surabaya. Jenis penelitian ini adalah kuantitatif. Pengambilan sampel dilakukan dengan teknik Multistage random sampling yaitu memilih sampel secara bertahap. Unit pertama adalah pengambilan minggu secara acak, kemudian hari dalam minggu yang sudah terpilih. Akhirnya Tterdapat 508 sampel suara pendengar yang diambil dalam tiga hari di bulan Februari 2013. Penelitian ini menggunakan metode analisis isi. Isi suara pendengar tentang lalu lintas dilihat melalui kategori saluran, topik lalu lintas, komponen lalu lintas, arah isi, dan jenis isi. Analisis yang digunakan adalah tabulasi silang untuk melihat hubungan antarvariabel. Dari hasil perbandingan tersebut diketahui bahwa suara pendengar tentang lalu lintas yang paling banyak dilaporkan adalah suara lalu lintas tentang kondisi lalu lintas (60,83%) dengan arah isinya netral (83,02%) dan jenisnya adalah informatif (87,20%). Dengan menggunakan saluran yang paling banyak digunakan oleh pendengar adalah saluran telepon (50,78%). Dari temuan-temuan tersebut menunjukkan bahwa pendengar radio Suara Surabaya memberikan suara secara aktif terkait informasi lalu lintas tentang kondisi lalu lintas dengan arah netral berjenis informatif dengan memanfaatkan saluran telepon Keyword : Suara Pendengar, Lalu Lintas, Radio, Analisis Is

Counting Hopf-Galois structures on cyclic field extensions of squarefree degree

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.We investigate Hopf-Galois structures on a cyclic field extension L/K of squarefree degree n. By a result of Greither and Pareigis, each such Hopf-Galois structure corresponds to a group of order n, whose isomorphism class we call the type of the Hopf-Galois structure. We show that every group of order n can occur, and we determine the number of Hopf-Galois structures of each type. We then express the total number of Hopf-Galois structures on L/K as a sum over factorisations of n into three parts. As examples, we give closed expressions for the number of Hopf-Galois structures on a cyclic extension whose degree is a product of three distinct primes. (There are several cases, depending on congruence conditions between the primes.) We also consider one case where the degree is a product of four primes.The first-named author acknowledges support from The Higher Committee for Education Development in Iraq

On insoluble transitive subgroups in the holomorph of a finite soluble group

This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: No data was used for the research described in the article.A question of interest both in Hopf-Galois theory and in the theory of skew braces is whether the holomorph Hol(N) of a finite soluble group N can contain an insoluble regular subgroup. We investigate the more general problem of finding an insoluble transitive subgroup G in Hol(N) with soluble point stabilisers. We call such a pair (G, N) irreducible if we cannot pass to proper non-trivial quotients G, N of G, N so that G becomes a subgroup of Hol(N). We classify all irreducible solutions (G, N) of this problem, showing in particular that every non-abelian composition factor of G is isomorphic to the simple group of order 168. Moreover, every maximal normal subgroup of N has index 2.Engineering and Physical Sciences Research Council (EPSRC

Scaffolds and Generalized Integral Galois Module Structure

This is the author accepted manuscript. The final version is available from the Association des Annales de l'Institut Fourier via the DOI in this record.Let L/K be a finite, totally ramified p-extension of complete local fields with residue fields of characteristic p > 0, and let A be a K-algebra acting on L. We define the concept of an A-scaffold on L, thereby extending and refining the notion of a Galois scaffold considered in several previous papers, where L/K was Galois and A = K[G] for G = Gal(L/K). When a suitable A-scaffold exists, we show how to answer questions generalizing those of classical integral Galois module theory. We give a necessary and sufficient condition, involving only numerical parameters, for a given fractional ideal to be free over its associated order in A. We also show how to determine the number of generators required when it is not free, along with the embedding dimension of the associated order. In the Galois case, the numerical parameters are the ramification breaks associated with L/K. We apply these results to biquadratic Galois extensions in characteristic 2, and to totally and weakly ramified Galois p-extensions in characteristic p. We also apply our results to the non-classical situation where L/K is a finite primitive purely inseparable extension of arbitrary exponent that is acted on, via a higher derivation (but in many different ways), by the divided power K-Hopf algebra

On the mixing properties of piecewise expanding maps under composition with permutations

This is the author accepted manuscript. The final version is available from American Institute of Mathematical Sciences via the DOI in this record.We consider the effect on the mixing properties of a piecewise smooth interval map f when its domain is divided into N equal subintervals and f is composed with a permutation of these. The case of the stretch-and-fold map f(x)=mxmod1 for integers m≥2 is examined in detail. We give a combinatorial description of those permutations σ for which σ∘f is still (topologically) mixing, and show that the proportion of such permutations tends to 1 as N→∞. We then investigate the mixing rate of σ∘f (as measured by the modulus of the second largest eigenvalue of the transfer operator). In contrast to the situation for continuous time diffusive systems, we show that composition with a permutation cannot improve the mixing rate of f, but typically makes it worse. Under some mild assumptions on m and N, we obtain a precise value for the worst mixing rate as σ ranges through all permutations; this can be made arbitrarily close to 1 as N→∞ (with m fixed). We illustrate the geometric distribution of the second largest eigenvalues in the complex plane for small m and N, and propose a conjecture concerning their location in general. Finally, we give examples of other interval maps f for which composition with permutations produces different behaviour than that obtained from the stretch-and-fold map

Skew braces of squarefree order

This is the author accepted manuscript. The final version is available from World Scientific Publishing via the DOI in this recordLet n ≥ 1 be a squarefree integer, and let M, A be two groups of order n. Using our previous results on the enumeration of Hopf-Galois structures on Galois extensions of fields of squarefree degree, we determine the number of skew braces (up to isomorphism) with multiplicative group M and additive group A. As an application, we enumerate skew braces whose order is the product of three distinct primes, in particular proving a conjecture of Bardakov, Neshchadim and Yadav on the number of skew braces of order 2pq for primes q > p ≥ 3

Hopf-Galois structures of squarefree degree

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordLet n be a squarefree natural number, and let G, Γ be two groups of order n. We determine the number of Hopf-Galois structures of type G admitted by a Galois extension of fields with Galois group isomorphic to Γ. We give some examples, including a full treatment of the case where n is the product of three primes