Authors:John Cossey; Yangming Li Pages: 533 - 537 Abstract: Let a finite group \(G=AB\) be the mutually permutable product of two p-soluble subgroups A and B for some prime p. We give a bound of the p-length of G from the p-lengths of A and B. PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1150-8 Issue No:Vol. 110, No. 6 (2018)

Authors:Jennifer Fidler; Daniel Glasscock; Brian Miceli; Jay Pantone; Min Xu Pages: 539 - 547 Abstract: We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given. PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1170-4 Issue No:Vol. 110, No. 6 (2018)

Authors:Lars Winther Christensen; Oana Veliche Pages: 549 - 562 Abstract: We identify minimal cases in which a power \(\mathfrak {m}^i\not =0\) of the maximal ideal of a local ring R is not Golod, i.e. the quotient ring \(R/\mathfrak {m}^i\) is not Golod. Complementary to a 2014 result by Rossi and Şega, we prove that for a generic artinian Gorenstein local ring with \(\mathfrak {m}^4=0\ne \mathfrak {m}^3\) , the quotient \(R/\mathfrak {m}^3\) is not Golod. This is provided that \(\mathfrak {m}\) is minimally generated by at least 3 elements. Indeed, we show that if \(\mathfrak {m}\) is 2-generated, then every power \(\mathfrak {m}^i\ne 0\) is Golod. PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1152-6 Issue No:Vol. 110, No. 6 (2018)

Authors:Shahram Rezaei Pages: 563 - 572 Abstract: Let R be a commutative Noetherian ring, \({\mathfrak {a}}\) an ideal of R, M a finitely generated R-module, and \({\mathcal {S}}\) a Serre subcategory of the category of R-modules. We introduce the concept of \({\mathcal {S}}\) -minimax R-modules and the notion of the \({\mathcal {S}}\) -finiteness dimension $$\begin{aligned} f_{\mathfrak {a}}^{{\mathcal {S}}}(M):=\inf \lbrace f_{\mathfrak {a}R_{\mathfrak {p}}}(M_{\mathfrak {p}}) \vert \mathfrak {p}\in {\text {Supp}}_R(M/ \mathfrak {a}M) \text { and } R/\mathfrak {p}\notin {\mathcal {S}} \rbrace \end{aligned}$$ and we will prove that: (i) If \({\text {H}}_{\mathfrak {a}}^{0}(M), \cdots ,{\text {H}}_{\mathfrak {a}}^{n-1}(M)\) are \({\mathcal {S}}\) -minimax, then the set \(\lbrace \mathfrak {p}\in {\text {Ass}}_R( {\text {H}}_{\mathfrak {a}}^{n}(M)) \vert R/\mathfrak {p}\notin {\mathcal {S}}\rbrace \) is finite. This generalizes the main results of Brodmann–Lashgari (Proc Am Math Soc 128(10):2851–2853, 2000), Quy (Proc Am Math Soc 138:1965–1968, 2010), Bahmanpour–Naghipour (Proc Math Soc 136:2359–2363, 2008), Asadollahi–Naghipour (Commun Algebra 43:953–958, 2015), and Mehrvarz et al. (Commun Algebra 43:4860–4872, 2015). (ii) If \({\mathcal {S}}\) satisfies the condition \(C_{\mathfrak {a}}\) , then $$\begin{aligned} f_{\mathfrak {a}}^{{\mathcal {S}}}(M)= \inf \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not } {\mathcal {S}}\hbox {-}minimax\rbrace . \end{aligned}$$ This is a formulation of Faltings’ Local-global principle for the \({\mathcal {S}}\) -minimax local cohomology modules. (iii) \( \sup \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not } {\mathcal {S}}\text {-minimax} \rbrace = \sup \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not in } {\mathcal {S}} \rbrace \) . PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1157-1 Issue No:Vol. 110, No. 6 (2018)

Authors:Claudia Schoemann; Stefan Wiedmann Pages: 573 - 580 Abstract: This note contains another proof of Grothendieck‘s theorem on the splitting of vector bundles on the projective line over a field k. Actually the proof is formulated entirely in the classical terms of a lattice \(\Lambda \cong k[T]^d\) , discretely embedded into the vector space \(V \cong K_\infty ^d\) , where \(K_\infty \cong k((1/T))\) is the completion of the field of rational functions k(T) at the place \(\infty \) with the usual valuation. PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1158-0 Issue No:Vol. 110, No. 6 (2018)

Authors:Necdet Batir Pages: 581 - 589 Abstract: We provide an elementary proof of the left-hand side of the following inequality and give a new upper bound for it. $$\begin{aligned} \bigg [\frac{n!}{x-(x^{-1/n}+\alpha )^{-n}}\bigg ]^{\frac{1}{n+1}}&<((-1)^{n-1}\psi ^{(n)})^{-1}(x) \\&<\bigg [\frac{n!}{x-(x^{-1/n}+\beta )^{-n}}\bigg ]^{\frac{1}{n+1}}, \end{aligned}$$ where \(\alpha =[(n-1)!]^{-1/n}\) and \(\beta =[n!\zeta (n+1)]^{-1/n}\) , which was proved in Batir (J Math Anal Appl 328:452–465, 2007), and we prove the following inequalities for the inverse of the digamma function \(\psi \) . $$\begin{aligned} \frac{1}{\log (1+e^{-x})}<\psi ^{-1}(x)< e^{x}+\frac{1}{2}, \quad x\in \mathbb {R}. \end{aligned}$$ The proofs are based on nice applications of the mean value theorem for differentiation and elementary properties of the polygamma functions. PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1156-2 Issue No:Vol. 110, No. 6 (2018)

Authors:Julian Scheuer Pages: 591 - 604 Abstract: To a real n-dimensional vector space V and a smooth, symmetric function f defined on the n-dimensional Euclidean space we assign an associated operator function F defined on linear transformations of V. F shall have the property that, for each inner product g on V, its restriction \(F_{g}\) to the subspace of g-selfadjoint operators is the isotropic function associated to f. This means that it acts on these operators via f acting on their eigenvalues. We generalize some well-known relations between the derivatives of f and each \(F_{g}\) to relations between f and F, while also providing new elementary proofs of the known results. By means of an example we show that well-known regularity properties of \(F_{g}\) do not carry over to F. PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1162-4 Issue No:Vol. 110, No. 6 (2018)

Authors:Geraldo Botelho; Ewerton R. Torres; Thiago Velanga Pages: 605 - 615 Abstract: We prove that every multipolynomial between Banach spaces is the composition of a canonical multipolynomial with a linear operator, and that this correspondence establishes an isometric isomorphism between the spaces of multipolynomials and linear operators. Applications to composition ideals of multipolynomials and to multipolynomials that are of finite rank, approximable, compact, and weakly compact are provided. PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1161-5 Issue No:Vol. 110, No. 6 (2018)

Authors:Guangwen Zhao Pages: 629 - 635 Abstract: We establish a volume decreasing result for V-harmonic maps between Riemannian manifolds. We apply this result to obtain corresponding results for Weyl harmonic maps from conformal Weyl manifolds to Riemannian manifolds. We also obtain corresponding results for holomorphic maps from almost Hermitian manifolds to quasi-Kähler manifolds, which generalize or improve the partial results in Goldberg and Har’El (Bull Soc Math Grèce 18(1):141–148, 1977, J Differ Geom 14(1):67–80, 1979). PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1160-6 Issue No:Vol. 110, No. 6 (2018)

Authors:Yiming Li; Lifeng Xi Abstract: For any Bedford-McMullen self-affine carpet, the geodesic path on the carpet between points \((x_{1},y_{1})\) and \((x_{2},y_{2})\) has length greater than or equal to \( x_{1}-x_{2} + y_{1}-y_{2} .\) This property fails for self-similar carpets. PubDate: 2018-06-01 DOI: 10.1007/s00013-018-1199-4

Abstract: Two different proofs are given showing that a quaternion algebra Q defined over a quadratic étale extension K of a given field has a corestriction that is not a division algebra if and only if Q contains a quadratic algebra that is linearly disjoint from K. This is known in the case of a quadratic field extension in characteristic different from two. In the case where K is split, the statement recovers a well-known result on biquaternion algebras due to Albert and Draxl. PubDate: 2018-05-30 DOI: 10.1007/s00013-018-1198-5

Authors:Mohammad Zarrin Abstract: In 1979, Herzog put forward the following conjecture: if two simple groups have the same number of involutions, then they are of the same order. We give a counterexample to this conjecture. PubDate: 2018-05-29 DOI: 10.1007/s00013-018-1195-8

Authors:Masaaki Amou; Keijo Väänänen Abstract: We prove algebraic independence of functions satisfying a simple form of algebraic Mahler functional equations. The main result (Theorem 1.1) partly generalizes a result obtained by Kubota. This result is deduced from a quantitative version of it (Theorem 2.1), which is proved by using an inductive method originated by Duverney. As an application we can also generalize a recent result by Bundschuh and the second named author (Theorem 1.2 and its corollary). PubDate: 2018-05-29 DOI: 10.1007/s00013-018-1196-7

Authors:Tesfa Mengestie Abstract: We study the topological structure of the space of Volterra-type integral operators on Fock spaces endowed with the operator norm. We prove that the space has the same connected and path connected components which is the set of all those compact integral operators acting on the spaces. We also obtain a characterization of isolated points of the space of the operators and show that there exists no essentially isolated Volterra-type integral operator. PubDate: 2018-05-14 DOI: 10.1007/s00013-018-1193-x

Authors:F. De Marchis; M. Grossi; I. Ianni; F. Pacella Abstract: For any smooth bounded domain \(\Omega \subset {\mathbb {R}}^2\) , we consider positive solutions to $$\begin{aligned} \left\{ \begin{array}{lr}-\Delta u= u^p &{} \text{ in } \Omega \\ u=0 &{} \text{ on } \partial \Omega \end{array}\right. \end{aligned}$$ which satisfy the uniform energy bound $$\begin{aligned}p\Vert \nabla u\Vert _{\infty }\le C\end{aligned}$$ for \(p>1\) . We prove convergence to \(\sqrt{e}\) as \(p\rightarrow +\infty \) of the \(L^{\infty }\) -norm of any solution. We further deduce quantization of the energy to multiples of \(8\pi e\) , thus completing the analysis performed in De Marchis et al. (J Fixed Point Theory Appl 19:889–916, 2017). PubDate: 2018-05-14 DOI: 10.1007/s00013-018-1191-z

Authors:Michela Egidi; Ivan Veselić Abstract: In this note we study the control problem for the heat equation on \(\mathbb {R}^d\) , \(d\ge 1\) , with control set \(\omega \subset \mathbb {R}^d\) . We provide a necessary and sufficient condition (called \((\gamma , a)\) -thickness) on \(\omega \) such that the heat equation is null-controllable in any positive time. We give an estimate of the control cost with explicit dependency on the characteristic geometric parameters of the control set. Finally, we derive a control cost estimate for the heat equation on cubes with periodic, Dirichlet, or Neumann boundary conditions, where the control sets are again assumed to be thick. We show that the control cost estimate is consistent with the \(\mathbb {R}^d\) case. PubDate: 2018-05-12 DOI: 10.1007/s00013-018-1185-x

Authors:S. Aivazidis; I. M. Isaacs Abstract: In this paper we study the family of finite groups with the property that every maximal abelian normal subgroup is self-centralizing. It is well known that this family contains all finite supersolvable groups, but it also contains many other groups. In fact, every finite group G is a subgroup of some member \(\Gamma \) of this family, and we show that if G is solvable, then \(\Gamma \) can be chosen so that every abelian normal subgroup of G is contained in some self-centralizing abelian normal subgroup of \(\Gamma \) . PubDate: 2018-05-12 DOI: 10.1007/s00013-018-1192-y

Authors:Grzegorz Graff Abstract: Let f be an \({\mathbb {R}}^n\) -diffeomorphism, where \(n=2,3\) , for which \(\{0\}\) is an isolated invariant set. We determine all possible forms of the sequences of fixed point indices of iterates of f at 0, \(\{\mathrm{ind}(f^n, 0)\}_n\) , confirming in \({\mathbb {R}}^3\) the conjecture of Ruiz del Portal and Salazar (J Differ Equ 249, 989–1013, 2010). PubDate: 2018-04-20 DOI: 10.1007/s00013-018-1180-2

Authors:Edward Grzegorek; Iwo Labuda Abstract: A theorem of Sierpiński says that every infinite set Q of reals contains an infinite number of disjoint subsets whose outer Lebesgue measure is the same as that of Q. He also has a similar theorem involving Baire property. We give a general theorem of this type and its corollaries, strengthening classical results. PubDate: 2018-04-13 DOI: 10.1007/s00013-018-1179-8