型为2~n的框架幂等Schrder拟群(英文)

Frame Idempotent Schrder Quasigroups of Type 2~n

摘要: 在一个v阶不完全的幂等Schro¨der拟群中去掉vi个阶为hi的子拟群(1≤i≤k),如果这些子拟群是不相交的且是生成的(即:∑1≤i≤kvihi=v),则称这个v阶拟群为框架幂等Schro¨der拟群,并记为FISQ(hv11h2v2…hvkk).业已证明,FISQ(1n)存在当且仅当n≡0,1(mod 4)且n≠5,9.本文报道了除n=8作为可能的例外,FISQ(2n)存在的充分必要条件是n≥5且n≠6.

Abstract: An incomplete idempotent Schro¨der quasigroup(IISQ)of ordervwithvimissing sub-IISQ(holes) of or-derhi(1≤i≤k),which are disjoint and spanning(i.e.,∑1≤i≤kvihi=v),is called a frame idempotent Schro¨der quasi-group and denoted by FISQ(h1v1h2v2…hkvk).It is known that an FISQ(1n)exists if and only ifn≡0,1(mod 4)andn≠5,9.It is proved that an FISQ(2n)exists if and only ifn≥5 andn≠6,with one possible exception thatn=8.