On Donovan's conjecture
On Donovan's conjecture
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关于多诺万的猜想
DOI：
10.1016/s0021-8693(03)00525-8
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发表时间：
2004
影响因子：
0.9
通讯作者：
Olaf Duevel
中科院分区：
文献类型：
--
作者：
Olaf Duevel
本文包含了Donovan猜想的一些较弱的变形的约化定理，它假设对每一个素数阶p的有限群D，只有1000个有限群的p-块的Morita等价类具有与D同构的亏群。(i)当把猜想限制在阿贝尔亏群的情况下时，它可以被简化为只考虑一类群的p-块，这些群接近于单群的直积。(ii)当把猜想限制在有限群的主块具有交换Sylow-p-子群的情况下，它可以简化为只考虑单群的p-块。Donovan猜想的一个较弱的版本假设，具有亏群同构于给定亏群的有限群的p-块的Cartan矩阵只有1000个。(iii)这个猜想可以简化为只考虑中心阶与p互素的拟单群的p-块。
This article contains reduction theorems for some weaker variants of Donovan's conjecture, which supposes that, for every finite group D of prime order p, there are only finitely many Morita equivalence classes of p-blocks of finite groups having defect groups isomorphic to D. (i) When restricting the conjecture to the case of abelian defect groups, it can be reduced to only considering p-blocks of a class of groups that are close to being direct products of simple groups. (ii) When restricting the conjecture to the case of principal blocks of finite groups having an abelian Sylow-p-subgroup, it can be reduced to only considering p-blocks of simple groups. A weaker version of Donovan's conjecture would suppose that there are only finitely many Cartan matrices of p-blocks of finite groups with defect group isomorphic to a given one. (iii) This conjecture can be reduced to only considering p-blocks of quasisimple groups with centers having orders prime to p.