The right angle to look at orthogonal sets
Logic
2016-07-07 v5
Abstract
If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developped. Moreover, a version of Schlichting's Theorem for hyperdefinable families of commensurable subgroups is shown.
Cite
@article{arxiv.1310.6275,
title = {The right angle to look at orthogonal sets},
author = {Frank Olaf Wagner},
journal= {arXiv preprint arXiv:1310.6275},
year = {2016}
}