ABSTRACT
Preview Activity 23.1. The family of groups denoted by Zn (where n is a positive integer) are the canonical examples of finite cyclic groups. In fact, it can be shown that, for each n ∈ Z+, Zn is the only cyclic group of order n. Recall that every element in Zn has the form [k]n = k[1]n for some integer k, so Zn is generated by [1]n-that is, Zn = 〈[1]n〉. (Note that, when the context is clear, we will typically omit subscripts and simply write Zn = 〈[1]〉.) One question we will address in this investigation is what the subgroup structure of Zn looks like. In other words, if H is a subgroup of Zn, what kind of things can we say aboutH? In this activity, we will consider the specific example whereH is a non-trivial subgroup of Z100.
