Two remarks on elementary theories of groups obtained by free constructions
Eric Jaligot (IF)
TL;DR
This paper generalizes previous results on elementary theories of groups formed by free constructions, focusing on their non-superstability and connectedness properties.
Contribution
It introduces two new generalizations: one on non-superstability and another on connectedness of free products of groups.
Findings
Most such groups are non-superstable.
Most free products of groups are connected.
Abstract
We give two slight generalizations of results of Poizat about elementary theories of groups obtained by free constructions. The first-one concerns the non-superstability of such groups in most cases, and the second-one concerns the connectedness of most free products of groups.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Topology and Set Theory · Advanced Operator Algebra Research