Free amalgamation and automorphism groups
release_64h6arvaa5cd5mkqgp7o5jdgqa
by
Andreas Baudisch
2014
Abstract
Let L be a countable elementary language, N be a Fraisse limit. We consider
free amalgamation for L-structures where L is arbitrary. If free amalgamation
for finitely generated substructures exits in N, then it is a stationary
independece relation in the sense of K.Tent and M.Ziegler [TZ12b]. Therefore
Aut(N) is universal for Aut(M) for all substructures M of N. This follows by a
result of I.M\"uller [Mue13] We show that c-nilpotent graded Lie algebras over
a finite field and c-nilpotent groups of exponent p (c < p) with extra
predicates for a central Lazard series provide examples. We replace the proof
in [Bau04] of the amalgamation of c-nilpotent graded Lie algebras over a field
by a correct one.
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