Zhang xingjian notes that subnormal conditions are weaker than that of normality and uses subnormal condition to replace the normal conditions . it follows that s - normality of a finite group is defined in " on s - normal subgroups of finite groups " ( to appear ) and many new results are obtained 张新建等在“ ons - normalsubgroupsoffinitegroups ” (待发表)一文已将c -正规中的有关条件削弱，引进了s -正规的概念，并且得到了一些新的重要结果。
2.
Then g is solvable if and only if there exists a solvable s - normal maximal subgroup m of g ; 3 ) let g be a finite group and mo = 1 where m is a maximal subgroup of g . then g is solvable if and only if m is a supersolvable s - normal subgroup of g and | g : m | = r where r is a prime 则g可解当且张新建:关于有限群的s一止规子群仅当g有一个可解s一正规极大子群m ; 3 )设g为有限群， m为g的极大子群且mg = l 。则g可解当且仅当m为g的超可解s一正规子群且} g : m = r其中r为素数。
