If $G$ is a group and $A,B$ are subgroups of it (or, I guess the definition just needs $A$ and $B$ to be subsets of $G$), what does $\langle A,B\rangle $ mean? I know what $\langle A\rangle $ means (just one set as argument) and I guess that $\langle A,B\rangle =\langle A\cup B\rangle $, but I just want to be sure. If someone can give me a precise definition, it would be very useful for me.
Thanks!
A not uncommon definition of $\langle A, B \rangle$, is simply $\langle A \cup B \rangle$. Another definitions of $\langle A ,B \rangle$ would be $$ \langle A ,B \rangle:= \bigcap_{A,B \subseteq H \in SG} H$$ where $SG$ is the set of subgroups of $G$. Of course these definitions can be extended to any number of sets.