TITLE: What does this notation mean: $\mathbb{Z}_2$
QUESTION [8 upvotes]: $\mathbb Z$ (Our usual notation for the integers) with a little subscript at the bottom. 
This is the question being asked:
what are the subgroups of order $4$ of $\mathbb Z_2 \times\mathbb Z_4$ ($\mathbb Z_2$ cross $\mathbb Z_4$)
Give them as sets and
identity the group of order 4 that each of the subgroup is isomorphic to
I was thinking that it meant the set of integers modulo $4$ and modulo $2$, but I'm not too sure 
Give them as sets and
identity the group of order $4$ that each of the subgroup is isomorphic to
What is the definition of "order". I couldn't really find that anywhere either.

REPLY [2 votes]: There is some ambiguity here. My text, Dummit and Foote, insists that $\mathbb Z_p$ is the cyclic group of order p, not the ring of integers modp. On this site, most often, $\mathbb Z_p$ refers to the ring of integers modp, and $C_p$ is the typical symbol for the cyclic group of order p. If you know, as in this case, that you are dealing with a group rather than a ring, the meaning is clear.