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In a paper of 2003, Külshammer, Olsson and Robinson defined ℓ-blocks for the symmetric groups, where ℓ>1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal ℓ-block. We then check that, in the Abelian case, we have an analogue of one of Broué's conjectures. [ABSTRACT FROM PUBLISHER]

We compare two Picard groups in dimension 1. Our proofs are constructive and the results generalize a theorem of J. Sands [11]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The article defines and investigates the new quasi-Stone algebras (QSA's) class. It characterizes the simple QSA's class and the class of irreducible QSA's which forms a primary class and with various locally finite QSA's. It points out the generation of various Stone algebras and Boolean algebras through a three-element Stone algebra and two-element Boolean algebra.

The article discusses the modal logic in finite model property. It describes the modal logic as a class of formulas that contains all classical tautologies and closed under the rule of substitution and material detachment. It also explains the property of sentential calculus which has a finite characteristic of matrix in the presence of positive integers.