Computer Search for Large Sets of Idempotent Quasigroups

摘要

A collection of n - 2 idempotent quasigroups of order n is called a large set if any two of them are disjoint, denoted by LIQ(n). While the existence of ordinary LIQ(n) has been extensively studied, the spectrums of large sets of idempotent quasigroups with various identities remain open, for example, large set of Steiner pentagon quasigroups of order 11 which is denoted by LSPQ(11). This paper describes some computer searching efforts seeking to solve such problems. A series of results are obtained, including the non-existence of LSPQ(11).