THE RELATIVIZED LASCAR GROUPS, TYPE-AMALGAMATION, AND ALGEBRAICITY

Abstract In this paper we study the relativized Lascar Galois group of a strong type. The is quasi-compact connected topological group, and if in addition underlying theory T G -compact, then compact. We apply compact to obtain model theoretic results note. For example, use divisibility type show that, simple theory, such types have certain property that call divisible amalgamation. main result c finite tuple algebraic over , $\operatorname {stp}(ac)$ abelian, groups {stp}(a)$ are isomorphic. To this, prove purely group-theoretic any abelian isomorphic its quotient by every subgroup. Several (counter)examples arising connection with theoretical development note presented as well. above, neither assumption nor being can be removed.