Tour:Introduction four (beginners)

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This page is part of the Groupprops guided tour for beginners (Jump to beginning of tour)
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General instructions for the tour | Pedagogical notes for the tour

In part one of the tour, we focused on basic definitions: group, subgroup, trivial group, and Abelian group. In part two, we tried to understand how to use the associativity, identity element and inverses to perform elementary manipulations in groups. In part three, we began understanding the subgroup structure of groups, the rules about intersections, unions and subgroups generated, and the notions of left and right coset.

This part of the tour is a preliminary look at some important classes of examples of groups, specifically, cyclic groups. We also pack here some general tools and approaches that will be useful later on.

Prerequisites for this part: Content covered in parts one, two, and three (or equivalent content). In particular, the definitions of group, subgroup, trivial group, Abelian group, identity element, inverses, intersection of subgroups, join of subgroups, generating set of a group, left coset of a subgroup. Also, the major facts proved about these.

Goal of this part: The goal here is a preliminary study an important class of groups: the cyclic groups. We study these from the viewpoint of how they occur naturally, and from the viewpoint of the generic tools we've developed for handling groups and subgroups.

This page is part of the Groupprops Guided tour for beginners (Jump to beginning of tour). If you found anything difficult or unclear, make a note of it; it is likely to be resolved by the end of the tour.
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