Changing the heights of automorphism towers by forcing with Souslin trees over L

@article{Fuchs2008ChangingTH,
title={Changing the heights of automorphism towers by forcing with Souslin trees over L},
author={G. Fuchs and J. D. Hamkins},
journal={Journal of Symbolic Logic},
year={2008},
volume={73},
pages={614 - 633}
}

Abstract We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid non-isomorphic Souslin trees whose isomorphism relation can be precisely controlled by forcing.