Resumo

CORTES-MEDINA, ADÁN  e  VALERO-ELIZONDO, LUIS. A computacional verification of Alperin's weight conjecture for groups of small order and their prime fields. Rev.colomb.mat. [online]. 2007, vol.41, n.2, pp. 325-331. ISSN 0034-7426.

Alperins Weight Conjecture was originally formulated for algebraically closed fields (see cite [1]). For some families of groups --such as the symmetric groups-- it is known to hold for arbitrary fields (see cite [2]), so it is reasonable to ask whether this conjecture holds for arbitrary fields, and in particular, if it holds for finite fields. We wrote computer software in MAGMA (see cite [8]) to test Alperins Weight Conjecture for finite fields, and tested this software on groups of small order and the prime fields whose characteristics divide the order of the groups. We found no counterexamples to this version of Alperins Conjecture for groups of order up to 100.

Palavras-chave : Group representation; Alperin's conjecture; weight; software; computational.