38 research outputs found
Essential idempotents and simplex codes
We define essential idempotents in group algebras and use them to prove that every mininmal abelian non-cyclic code is a repetition code. Also we use them to prove that every minimal abelian code is equivalent to a minimal cyclic code of the same length. Finally, we show that a binary cyclic code is simplex if and only if is of length of the form and is generated by an essential idempotent
The smallest simple Moufang loop
We study the simple Moufang loop GLL(F(2)) and give a complete description of its lattice of subloops. (C) 2008 Elsevier Inc. All rights reserved
Locally nilpotent groups of units in tiled rings
We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.CNPqConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP of BrazilFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP
Groups, rings and group rings
Table of Contents Forthcoming