超越古典背景的施赖尔重写
Schreier rewriting beyond the classical setting
摘要：
利用自由幺半群和自由结合代数的作用，建立了自由作用中作用的秩和子作用的秩的Schreier型公式，以及自由作用的子作用的交的秩的Grassmann型关系.利用自由群的陪集作用，将Schreier公式推广到无穷指数子群的情形.我们还研究和应用自由结合代数上的大模，在论文的精神Olshanskii，A。余。Osin，D.V.，大群及其周期性的变化，美国数学学会会刊，136（2008），753 - 759.
英文摘要：
Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving the ranks of actions and the ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish the generalization of the Schreier formula to the case of subgroups of infinite index. We also study and apply large modules over free associative algebras in the spirit of the paper Olshanskii, A. Yu.; Osin, D.V., Large groups and their periodic quotients, Proc. Amer. Math. Soc., 136 (2008), 753 - 759.
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