In
mathematical group theory, a tame group is a certain kind of
group defined in
model theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...
.
Formally, we define a bad field as a structure of the form (''K'', ''T''), where ''K'' is an
algebraically closed field and ''T'' is an
infinite, proper, distinguished
subgroup of ''K'', such that (''K'', ''T'') is of finite
Morley rank In mathematical logic, Morley rank, introduced by , is a means of measuring the size of a subset of a model of a theory, generalizing the notion of dimension in algebraic geometry.
Definition
Fix a theory ''T'' with a model ''M''. The Morley rank ...
in its full language. A group ''G'' is then called a tame group if no bad field is
interpretable in ''G''.
References
* A. V. Borovik, Tame groups of odd and even type, pp. 341–-366, in ''Algebraic Groups and their Representations'', R. W. Carter and J. Saxl, eds. (NATO ASI Series C: Mathematical and Physical Sciences, vol. 517),
Kluwer Academic Publishers, Dordrecht, 1998.
Model theory
Infinite group theory
Properties of groups
{{algebra-stub