Hebrew University

Amitsur Algebra Seminar
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Time: Thursday, Dec 15, 12:00 - 13:15
Place: math 209

Speaker: Doron Puder (HUJI)

Title:  Primitive Words in Free Groups (Cont.)

Abstract:

This is a sequel of the Colloquium talk from 8.12.2011.  We shall try
to convey the main ideas of the proof of the results mentioned below.

We consider two properties of words in F_k, the free group on k
generators. A word w is called primitive if it belongs to a basis (i.e. a
free generating set) of F_k. It is called measure preserving if for every
finite group G, all elements of G are obtained by the word map $w : G^k \to G$ the same number of times.

It is an easy observation that a primitive word is measure preserving.
Several mathematicians, most notably from Jerusalem, have conjectured that
the converse is also true. After proving the special case of F_2, we
manage to prove the conjecture in full in a recent joint work with O.
Parzanchevski. As an immediate corollary, we prove another conjecture and
show that the set of primitive words in F_k is closed in the profinite
topology.

Different tools are used in the proof, including Stallings core graphs,
random coverings of graphs, Mobius inversions and algebraic extensions of
free groups. The proof also involves a new algorithm to detect primitive
words and a new categorization of free words.

You are cordially invited!

<http://math.huji.ac.il/amitsur.html>

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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il>
Announcement from: Gili Schul   <gili.schul@mail.huji.ac.il>