The Existence of a Large Set of Idempotent Quasigroups of Order $62$

Abstract

In this article, we construct a large set of idempotent quasigroups of order 62. The spectrum for large sets of idempotent quasigroups of order $n$ (briefly, $LQ(n)$) is the set of all integers $n\ge 3$ with the exception $n=6$ and the possible exception $n=14$.