(c) Let V≠0 be a faithful and completely reducibleF[G]-module over an arbitrary field F.
(c)若V≠0是任意域F上的一忠实且完全可约F[G]模。
completely reducible,quasi-primitive and finite G-module for a solvable group G.
证明了可解群阶的定理:令V≠0是有限拟本原G 模,|V|=qn,素数q>0,G为完全线性群GL(V)的一可解完全可约子群,则a)|G|≤|V|α/λ,b)若2 |G|,且q≠2,则|G|≤|V|3/2/241/3。
Improves the theorem “A finite poset is dismantlable if and only if it is dismantlable by irreducibles”, obtains a new theorem “A finite poset is homotopic dismantlable if and only if it is dismantlable by star irreducibles” and proves the equivalence of these theorems.
就Ｆｉｘｅｄ Ｐｏｉｎｔ ｉｎ Ｐｏｓｅｔ中的定理“有限偏序集Ｐ是可拆的充要条件为Ｐ是不可约可拆”进行了改进，得到了Ｐ是同伦可拆的充要条件为Ｐ是星形不可约可拆，并且证明了这两个充要条件等价，极大地简化了不可约可拆的判别