| Popis: |
We construct infinite groups by taking a canonical set of generators for the general linear group over the ring Zpn and generalising these to a group of linear maps on an R-module, where R is any ring with a 1. The structure of the groups obtained is related to the structure of the Jacobson radical of the ring, and we show that the groups considered have a wide range of generalised nilpotent properties. We show that our construction can yield infinite simple groups. As far as the author knows these groups have not previously been studied. We prove that many of the groups are SI-groups having subgroups which are not SI-groups. Previously only one example of such a group seems to have been known. The last chapter of this thesis is concerned with a completely different class of infinite groups. We construct here infinite groups that are generalisations of the Sylow p-subgroup of the symplectic group. The main result obtained is the construction of a group having two ascendant Abelian subgroups whose join is self-normalising. Again only one example of such a group seems to have been known previously. |
