%%visits: 4 ## intuition== We can extend the generator notation to accommodate two symbols, for example ⟨a, b⟩, which can make an infinite list of elements in the group generated by this ({a, b, ab, aba, abab, …} or {a, ab, aab, aaab, aaaab, aaaaab, …} or any other combination you can think of
“Clearly ⟨a⟩ ⊂ ⟨a, b⟩ and ⟨b⟩ ⊂ ⟨a, b⟩, ⟨a, b⟩ is the intersection of all subgroups containing both a and b.”
tags :math:groups_and_symmetries:introduction_to_abstract_algebra: