Schreier rewriting beyond the classical setting

Details Schreier rewriting beyond the classical setting Schreier rewriting beyond the classical setting

2008-11-09

arxiv.org/abs/0811.1336v1

Mathematics

Rings and Algebras

17 pages

Scientific paper

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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