Quoting John Conway <conway@Math.Princeton.EDU>:
The easiest (because weakest) statement is that every finite group is a direct product of indecomposable groups, and that the isomorphism types of these groups are uniquely determined up to order. ["Indecomposable" means "not a direct product of two non-trivial groups"].
I hope that I haven't blundered into a conversation which I don't understand, but since I have been struggling with this while trying to identify reversible cellular automata, I thought I'd express my doubts to see where my thinking has gone wrong. The version I have is that every finite group is a subgroup of a wreath product of some factor group and its kernel. Of course, if there is no normal subgroup there is no decomposition. The definition of indecomposable above implies <two> normal subgroups, not <one>, but then that would make an awful lot of groups indecomposable that otherwise have a perceptible structure. Like semidirect products. Does the "weakness" alluded to above mostly mean that abelian groups, which have lots of normal subgroups, are being classified? Can anyone reccommend a nice, introductory, treatment of wreath products and Krohn-Rhodes decompositions? - hvm ------------------------------------------------- Obtén tu correo en www.correo.unam.mx UNAMonos Comunicándonos