We show that two metacyclic groups of the following types are isomorphic if they have the same character tables: (i) split metacyclic groups, (ii) the metacyclic p-groups and (iii) the metacyclic {p, q}-groups, where p, q are odd primes. 2010 Mathematics Subject Classification. Primary 20C15; Secondary 20D15, 20F16, 20F22.

It has been shown that for distinct odd primes p1, p2, . . . , pn and q, all Moufang loops of order p1p2 · · · pnq are groups if and only if q is not congruent to 1 modulo pi for each i. In this paper, we extend that result to include Moufang loops of order p1p 2 2 · · · pnq. Mathematics Subject Classification: 20N05

JEL classification: C65, D63, D71, D81 Mathematics Subject Classification (2000): 91B16

The main goal of this survey is the description of the fruitful interaction between Ergodic Theory and Number Theory via the study of two beautiful results: the first one by Ben Green and Terence Tao (about long arithmetic progressions of primes) and the second one by Noam Elkies and Curtis McMullen (about the distribution of the sequence {√n}mod 1). More precisely, during the first part, we wi...

* Correspondence: [email protected] Department of Mathematics, China Three Gorges University, Yichang, 443002, China, Abstract Lutwak proposed the notion of Lp-geominimal surface area according to the Lpmixed volume. In this article, associated with the Lp-dual mixed volume, we introduce the Lp-dual geominimal surface area and prove some inequalities for this notion. 2000 Mathematics Subject Cla...

AMS Mathematics Subject Classification (2000): 46B03, 46B05

AMS Mathematics Subject Classification (2000): 05C50

AMS Mathematics Subject Classification (2000): 34G10

Mathematics Subject Classification (2000): 53C25, 53C40, 53C42.

AMS Mathematics Subject Classification (2000): 05C50