Subquasigroup of size more than half is whole quasigroup

Statement

If $Q$ is a quasigroup of order $n$ and $S$ is a subquasigroup of order $s$ then $2s\le n$.

Related facts

• Subgroup of size more than half is whole group
• Lagrange's theorem

References

• *Wall, Drury W.: Sub-Quasigroups of Finite Quasigroups, Pacific Journal of Mathematics Volume 7, Number 4 (1957), 1711-1714