This BSc thesis deals with certain topics from group theory. We investigate group actions and in particular devote most of our attention to the research of blocks of imprimitivity and their characteristics. This is a very important concept in the theory of permutation groups, since the existence of the so-called imprimitivity block system for a given action, often enables us to reduce the action to a much smaller set, which makes it more manageable.
In the thesis, we collect the basic notions and results that are necessary for the understanding of the central theme. We review some basic facts about group actions and their properties and present some examples. We introduce the concept of a block of imprimitivity, we explore the criterion for their existence and we give some examples of them. We link the concept of blocks of imprimitivity with the concept of an imprimitive action and present necessary and sufficient conditions for the action to be primitive or imprimitive. We present examples of primitive and imprimitive group actions and explore the connection between intransitive normal subgroups and blocks of imprimitivity.
|
