A new characterization of A 5

Let G be a group and τ _e (G) the set of numbers of elements of G of the same order. In this paper, by τ _e (G), we give a new characterization of A ₅, where A ₅ is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, ${G\cong A_5}$ if and only if τ _e (G) = τ _e (A ₅) = {1, 15, 20, 24}.     

方阵开n次方的一个实用准则

得出了由方阵Ａ的幂秩判定Ａ能否开ｎ次方的一个实用准则,同时也获得了确定Ａ的约旦标准形结构的一个结果。     

A generalization of a theorem of A. Grothendieck

In this article we characterize the quasi‐barrelledness of the projective tensor product of a coechelon space of type one k ¹(A) with a Fréchet space, including homological conditions as exactness properties of the corresponding tensor product functor k ¹(A) ·: ? → ??, acting from the category of Fréchet spaces to the category of linear spaces, resp. the vanishing of its first right derivative Tor¹_π (k ¹(A),.). This generalizes and extends a classical theorem of A. Grothendieck ([13, Chap. II, §4, No. 3, Theorem 15]). Further we present an analogous theorem for complete coechelon spaces of type zero and the injective tensor product and results concerning the stronger property of barrelledness. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A theorem of Yu. A. Aminov

We give a simple proof of a somewhat stronger theorem of Yu. A. Aminov concerning a lower estimate of the diameter of a surface immersed in R, this estimate being a function of the mean curvature of the surface and of its Ricci curvature. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 45, pp. 53–55, 1974.     

A problem of A. I. Mal'tsev

Erevan. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 6, pp. 3–11, November–December, 1988.     

A theorem of A. G. Vitushkin

An important condition for the coincidence of the algebras R(E) and C(E) on a compactum was found by A. G. Vitushkin. In this note we give a simple proof of Vitushkin's theorem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 178–181, 1984.     

A generalization of A. Connes' trace formula

A new Bessel type function is found for each field of p-adic numbers, which has remarkable properties. By using this Bessel function, a Hankel type transformation is defined for every field of p-adic numbers. It is the analogue of the classical Hankel transformation of order zero (Li, 2007 [8]). A global Hankel transformation is defined on the adele group. It is closely related to the Euler product formula of the Riemann zeta function. Local and S-local trace formulas are obtained for the Hankel transformation. They are generalizations of A. Connes' corresponding trace formulas in Connes (1999) [5].     

A question of L. A. Shemetkov

Translated fromAlgebra i Logika, Vol. 31, No. 6, pp. 624–636, November–December, 1992.