# Groups of order 1

From Groupprops

This article gives information about, and links to more details on, groups of order 1

See pages on algebraic structures of order 1| See pages on groups of a particular order

There is, up to isomorphism, a unique group of order 1, namely the trivial group. In fact, it is, up to isomorphism, the unique *magma* of order 1. We can see this by noting that the multiplication table on any one-element set is completely constrained.