\titleofpresentation{A construction of non-tame automorphisms of a
  free group
of rank 3 in the variety ${\bf A}_{p}{\bf A}$}

\presenter{A. I. Papistas}

Let $F_{3}$ be a free group of rank $3$. For a
non-negative integer $m$, ${\bf A}_{m}$ denotes the variety of all
abelian groups of exponent of dividing $m$, interpreted in such a
way that ${\bf A}_{0} = {\bf A}$ is the variety of all abelian
groups. Write ${\bf V}_{m}$ for the variety of all extensions of
groups in ${\bf A}_{m}$ by groups in ${\bf A}$. For a prime
integer $p$, let $M_{3} = F_{3}({\bf V}_{p})$. The natural mapping
from $F_{3}$ onto $M_{3}$ induces a homomorphism $\alpha$ from
${\rm Aut}(F_{3})$ into ${\rm Aut}(M_{3})$. An automorphism of
$M_{3}$ which belongs to the image of $\alpha$ is called tame. We
give a way of constructing non-tame automorphisms of $M_{3}$.

\presenteraddress{Aristotle University of Thessaloniki,
Faculty of Science,
Department of Mathematics,
GR 541 21, Thessaloniki,
Greece}

\email{apapist@math.auth.gr}






