摘要
１９７８年，Ｄ，Ｑｕｉｌｌｅｎ证明了：若群Ｇ有非平凡的正规ｐ－子群，则由ｐ－子群组成的半序集是可缩的。同时，他还猜想逆定理也成立。１９９３年，Ｍ．Ａｓｃｈｂａｃｈｅｒ和Ｓ．Ｄ．Ｓｍｉｔｈ证明了若群Ｇ不包含某种酉分支的话，则Ｑｕｉｌｌｅｎ猜想的确成立，在他们的证明中，Ｑｕｉｌｌｅｎ所证明的下述定理起着很重要的作用：由基本阿贝耳Ｐ－子群组成的半序集到所有Ｐ－子群组成的半序集的包含映射导出对应下同调的同构。以Ｂｕｃｈｓｂａｕｍ条件为重要的工具，本文将重新叙述此定理的证明。
In 1978 D. Quillen proved that if a finite group G has a nontrivial normal p-subgroup,then the poset of p-subgroups of G is contraictible. At the same time he conjecturedthe converse.In 1993,M. Aschbacher and S.D. Smith proved the conjecture to be true,exceptPossibly when certain unitary components are present. A key tool in this proof is Quillen’stheorem that the inclusion of the poset of elementary abelian p-subgroups into the poset of allp-subgroups of G induces isomorphisms in honiology. The present paper revisits this proof, withspecial emphaisis on“Bushcbaum’s criterion.”
出处
《数学进展》
CSCD
北大核心
1995年第6期501-514,共14页
Advances in Mathematics（China）
