A group is called cyclic if it is generated by a single element, that is. In this paper i draw upon a few images of number theory as a queen and as a servant of mathematics. A finite cyclic group with n elements is isomorphic to the additive group zn of integers modulo n. Find materials for this course in the pages linked along the left. If youre a math major, then you probably want to pass. A group is abelian2 if ab bafor all 2 also known as commutative a, bin g. The second list of examples above marked are nonabelian. Furthermore, i focus on this duality of number theory as it.
A friendly introduction to group theory mathematics. The galois group of the polynomial fx is a subset galf. A cyclic group can be generated by a generator g, such that every other element of the group can be written as a power of the generator g. Every group galways have gitself and eas subgroups. Pdf this chapter is a concise mathematical introduction into the algebra of groups. This book is designed for a first course in group theory. Like any good mathematical game, group theory is almost cartoonishly simple at. Freely browse and use ocw materials at your own pace.
The current module will concentrate on the theory of groups. A group gis called abelian or commutative if gh hg for all g. Snf closed with respect to the composition and inversion of maps, hence it forms a group in the sense of def. When ever one studies a mathematical object it is important to know when two representations of that object. For example, multiplication and addition are binary operations. Finite groups sam kennerly june 2, 2010 with thanks to prof. Jelena mari cic, zechariah thrailkill, travis hoppe. It is build up in the way that definitions are followed.