Symmetric Units and Group Identities in Group Algebras

We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity

Structure of normal twisted group rings

Let K(lambda)G be the twisted group ring of a group G over a commutative ring K with 1, and let lambda be a factor set (2-cocycle) of G over K. Suppose f:G —> U(K) is a map from G onto the group of units U(K) of the ring K satisfying f(1) = 1. If x = Sigma(g is an element of G)alpha(g)u(g) is an element of K(lambda)G then we denote Sigma(g is an element of G)alpha(g)f(g)u(g)(-1) by x(f) and assume that the map x —> x(f) is an involution of K(lambda)G. In this paper we describe those groups G and commutative rings K for which K(lambda)G is f-normal, i.e. xx(f)=x(f)x for all x is an element of K(lambda)G

Factors behind high cash usage in Hungary

This article summarises the findings of qualitative, in-depth interviews which aimed to explore the motivating factors behind domestic cash usage that generate the significantly higher cash volumes in Hungary than would ’normally’ be justified. In the opinion of the experts interviewed, cash usage may be facilitated by the intensive cash need of the hidden economy, the traditional cash-oriented behaviour of the public administration and a lack of trust in business-to-business transactions. This analysis primarily intends to capture certain trends, which may have temporarily changed in the wake of the economic crisis, but nevertheless span a number of years and the specific phenomena of which may be regarded as generally valid over the long term, apart from certain periodic effects.cash usage, hidden economy, tax avoidance, petty cash.

Csoportgyűrűk = Group rings

A következő témakörökben értünk el eredményeket: - algebrák reprezentációelmélete (vizsgáltuk Lie-algebrák burkoló algebrájának filteres multiplikatív bázisát) - véges csoportok reprezentációelmélete és az egész számok feletti csoportgyűrűk egységcsoportja (vizsgáltuk Zassenhaus sejtését, azaz hogy az egész számok csoportgyűrűjének minden torzió egysége racionálisan konjugált az alapcsoport valamely elemével. Leírtuk a GL(n,K) lineáris csoportnak a felbonthatatlan nem ciklikus negyedrendű részcsoportjait, ahol K vagy az egész számok gyűrűje, vagy lokalizációja 2 prím szerint, vagy a 2-adikus egész számok gyűrűje) - csoportalgebrák és keresztszorzatok (vizsgáltuk a csoportalgebrák és keresztszorzatok Lie nilpotenciáját, és ezeknek a Lie nilpotencia indexét, továbbá a KG csoportalgebra V(KG) egységcsoportjának a struktúráját, ahol G egy p-csoport és K egy p karakterisztikájú test) - csoportalgebrák és csoportgyűrűk egységcsoportja (leírtuk, hogy mikor lesz az egységcsoport hiperbolikus Gromov értelemben, és mikor lesz az egységcsoport teljes hatványú p-csoport) - komputer algebra (továbbfejlesztettük és elkészítettük egy újabb verzióját a GAP komputer algebra rendszer LAGUNA program csomagjának (verziószáma: 3.5.0)) | We obtained new results in the following topics: 1. Representation theory of algebras. We studied filtered multiplicative bases of enveloping algebras of Lie algebras. 2. Representation theory of finite groups and unit groups of integral group rings. We studied the Zassenhaus conjecture, which states that every torsion element of ZG is rationally conjugate to an element of G. We described the indecomposable non cyclic subgroups of order four of the linear group GL(n,K), where K is either the ring of integers, or its localization at the prime 2, or the ring of 2-adic integers. 3. Group rings and crossed products. We studied their Lie nilpotency and their Lie nilpotency indices, and also the structure of the unit group V(KG) of KG, where G is a p-group and the field K has characteristic p. 4. Unit groups of group rings and algebras. We determined those cases when the unit group is hyperbolic in Gromov's notation, and we described the cases when the unit group is a powerful p-group. 5. Computer algebra. We developed a new and more powerful version (numbered as 3.5.0) of the LAGUNA computer algebra package of the GAP system

Integral group ring of the McLaughlin simple group

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs

Integral group ring of the first Mathieu simple group

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Mathieu group M11. As a consequence, for this group we confirm the conjecture by Kimmerle about prime graphs

Amplitude variations of modulated RV Tauri stars support the dust obscuration model of the RVb phenomenon

Context. RV Tauri-type variables are pulsating post-AGB stars that evolve rapidly through the instability strip after leaving the Asymptotic Giant Branch. Their light variability is dominated by radial pulsations. Members of the RVb subclass show an additional variability in form of a long-term modulation of the mean brightness, for which the most popular theories all assume binarity and some kind of circumstellar dust. Here we address if the amplitude modulations are consistent with the dust obscuration model. Aims. We measure and interpret the overall changes of the mean amplitude of the pulsations along the RVb variability. Methods. We compiled long-term photometric data for RVb-type stars, including visual observations of the American Association of Variable Star Observers, ground-based CCD photometry from the OGLE and ASAS projects and ultra-precise space photometry of one star, DF Cygni, from the Kepler space telescope. After converting all the observations to flux units, we measure the cycle-to-cycle variations of the pulsation amplitude and correlate them to the actual mean fluxes. Results. We find a surprisingly uniform correlation between the pulsation amplitude and the mean flux: they scale linearly with each other for a wide range of fluxes and amplitudes. It means that the pulsation amplitude actually remains constant when measured relative to the system flux level. The apparent amplitude decrease in the faint states has long been noted in the literature but it was always claimed to be difficult to explain with the actual models of the RVb phenomenon. Here we show that when fluxes are used instead of magnitudes, the amplitude attenuation is naturally explained by periodic obscuration from a large opaque screen, one most likely corresponding to a circumbinary dusty disk that surrounds the whole system.Comment: 8 pages, 6 figures, accepted for publication in A&

Képfeledettség és kultúrpesszimizmus, Varga Emőke, Az illusztráció a teóriában, a kritikában, az oktatásban

K

Et in Arcadia ego és felboncollak

A tanulmány a képzőművészet és az anatómia kapcsolatát tárgyalja az 1803-ban Velencében kiadott Tabulae anatomicae ligamentorum corporis humani… című kötet belső címlapjához helyezett metszet segítségével, ami közelebb visz az "Et in Arcadia ego" Kazinczy által is használt, a 18-19. század fordulóján Európa-szerte a képzőművészetekben és az irodalomban is használt formulájának megértéséhez