论文标题
与原始替代相关的Pronilpotent商
Pronilpotent quotients associated with primitive substitutions
论文作者
论文摘要
我们描述了使用特殊类型的演示文稿定义的一类投射涂鸦群的一类投射涂鸦群的发起人。 $ω$呈现的组的倾斜商完全由单个多项式确定，与矩阵的特征多项式密切相关。我们推断出$ω$的群体是完美的，或者承认$ p $ - adiC整数是许多素数的商品。我们还发现了$ω$呈现的$ω$ freeness的必要条件。我们的主要动机来自Semigroup理论：与原始取代相对应的自由profinite单体的最大亚组为$ω$呈现（由于Almeida和Costa引起的定理）。我们能够证明原始替代的发射矩阵带有有关相应最大亚组的倾斜商的部分信息。我们将其应用于推断与对应于恒定长度的原始大道取代的最大亚组并非绝对免费。
We describe the pronilpotent quotients of a class of projective profinite groups, that we call $ω$-presented groups, defined using a special type of presentations. The pronilpotent quotients of an $ω$-presented group are completely determined by a single polynomial, closely related with the characteristic polynomial of a matrix. We deduce that $ω$-presented groups are either perfect or admit the $p$-adic integers as quotients for cofinitely many primes. We also find necessary conditions for absolute and relative freeness of $ω$-presented groups. Our main motivation comes from semigroup theory: the maximal subgroups of free profinite monoids corresponding to primitive substitutions are $ω$-presented (a theorem due to Almeida and Costa). We are able to show that the incidence matrix of a primitive substitution carries partial information on the pronilpotent quotients of the corresponding maximal subgroup. We apply this to deduce that the maximal subgroups corresponding to primitive aperiodic substitutions of constant length are not absolutely free.
