Real characters in blocks

We consider real versions of Brauer's k(B) conjecture, Olsson's conjecture and Eaton's conjecture. We prove the real version of Eaton's conjecture for 2-blocks of groups with cyclic defect group and for the principal 2-blocks of groups with trivial real core. We also characterize G-classes, real and rational G-classes of the defect group of a block B

Cartan Invariants and Central Ideals of Group Algebras

Abstract. In this paper we investigate general properties of Cartan invariants of a finite group G in characteristic 2. One of our results shows that the Cartan matrix of G in characteristic 2 contains an odd diagonal entry if and only if G contains a real element of 2-defect zero. We also apply these results to 2-blocks of symmetric groups and to blocks with normal or abelian defect groups. The second part of the paper deals with annihilators of certain ideals in centers of group algebras and blocks

Central Ideals and Cartan Invariants of Symmetric Algebras

In this paper, we investigate certain ideals in the center of a symmetric algebra A over an algebraically closed eld of characteristic p > 0. These ideals include the Higman ideal and the Reynolds ideal. They are closely related to the p-power map on A. We generalize some results concerning these ideals from group algebras to symmetric algebras, and we obtain some new results as well. In case p = 2, these ideals detect odd diagonal entries in the Cartan matrix of A. In a sequel to this paper, we will apply our results to group algebras

Cartan Invariants and Central Ideals of Group Algebras

Abstract. In this paper we investigate general properties of Cartan invariants of a finite group G in characteristic 2. One of our results shows that the Cartan matrix of G in characteristic 2 contains an odd diagonal entry if and only if G contains a real element of 2-defect zero. We also apply these results to 2-blocks of symmetric groups and to blocks with normal or abelian defect groups. The second part of the paper deals with annihilators of certain ideals in centers of group algebras and blocks

Triterpenes in Traditional and Supercritical-Fluid Extracts of Morus alba Leaf and Stem Bark

Our objectives were to establish a GC method capable of quantitative analysis of terpenoids without derivatisation and to examine the amount of beta-sitosterol extracted from Morus alba L. leaf and stem bark by use of traditional organic solvent extraction and supercritical-fluid extraction (SFE). To measure beta-sitosterol content without derivatization, GC-FID was used with 5-alpha-cholestan-3-one as internal standard. To identify terpenoid constituents, GC-MS was used; beta-sitosterol, phytol, lanost-7-en-3-on, alpha-amyrin, beta-amyrin, and lupeol were identified. We established that for Morus leaf the best SFE method for beta-sitosterol was pilot scale SFE; the beta-sitosterol content of this extract was higher than that of the hexane solvent extract. Among analytical SFE conditions, 200 bar for 90 min and 300 bar for 60 min resulted in extraction of the most beta-sitosterol. For mulberry stem bark, solvent extraction with hexane and SFE at 400 bar and 40 degrees C for 60 min proved the best methods