arXiv subjects

Alexander Olshanskii

Publications and source records attributed to Alexander Olshanskii.

21 records · Page 2Linked to original sources

arXiv2008

Schreier rewriting beyond the classical setting

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.

math.RA↗

arXiv2006

Large Restricted Lie Algebras

We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which can serve as counterexamples for various Burnside-type questions.

math.RA↗

arXiv2005

Groups with small Dehn functions and bipartite chord diagrams

We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function $n^2\log n$ and other small Dehn functions. Some of these groups have undecidable conjugacy problem.

math.GR↗