Schreier rewriting beyond the classical setting |
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| Authors: | Yuri Bahturin Alexander Olshanskii |
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| Institution: | (1) Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada;(2) Department of Algebra, Faculty of Mathematics and Mechanics, 119899 Moscow, Russia;(3) Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA |
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| Abstract: | Using actions of free monoids and free associative algebras, we establish some Schreiertype formulas involving ranks of actions
and 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 a generalization of the Schreier formula in the case of subgroups
of infinite index. We also study and apply large modules over free associative and free group algebras.
This work was supported by Natural Sciences and Engineering Research Council of Canada (Grant No. 227060-04), Yuri Bahturin,
National Science Foundation (Grant No. DMS-0700811) and Russian Fund for Basic Research (Grant No. 08-01-00573), Alexander
Olshanskii |
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| Keywords: | free algebra group monoid act G-set module |
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