Quotients of locally minimal groups

2019 ◽  
Vol 475 (2) ◽  
pp. 1215-1241 ◽  
Author(s):  
Dekui Peng ◽  
Dikran Dikranjan ◽  
Wei He ◽  
Zhiqiang Xiao ◽  
Wenfei Xi
Keyword(s):  
Minimal Groups

scholarly journals ON THE STRUCTURE OF GROUPS ENDOWED WITH A COMPATIBLE C-RELATION

2018 ◽  
Vol 83 (3) ◽  
pp. 939-966
Author(s):  
GABRIEL LEHÉRICY
Keyword(s):  
Ordered Groups ◽  
Quasi Order ◽  
Minimal Groups

AbstractWe use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of quasi-orders some results concerning C-minimal groups given in [5].

scholarly journals ON REGULAR GROUPS AND FIELDS

2014 ◽  
Vol 79 (3) ◽  
pp. 826-844 ◽  
Author(s):  
TOMASZ GOGACZ ◽  
KRZYSZTOF KRUPIŃSKI
Keyword(s):  
Conjugacy Class ◽  
Classical Group ◽  
Multiplicative Group ◽  
Finite Extension ◽  
Generic Type ◽  
Common Generalization ◽  
Counter Example ◽  
Minimal Groups ◽  
Unbounded Orbit

AbstractRegular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenP(n)has unbounded orbit under the action of the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable.

Emotions of my kin: disambiguating expressive body movement in minimal groups

2016 ◽  
Vol 4 (1) ◽  
pp. 51-71 ◽  
Author(s):  
Gary Bente ◽  
Daniel Roth ◽  
Thomas Dratsch ◽  
Kai Kaspar
Keyword(s):  
Body Movement ◽  
Minimal Groups ◽  
Expressive Body Movement

scholarly journals On non-abelian C-minimal groups

2003 ◽  
Vol 122 (1-3) ◽  
pp. 263-287 ◽  
Author(s):  
Patrick Simonetta
Keyword(s):  
Minimal Groups

Perceptual accentuation in minimal groups

1987 ◽  
Vol 17 (3) ◽  
pp. 347-352 ◽  
Author(s):  
Lawrence G. Herringer ◽  
Raymond T. Garza
Keyword(s):  
Minimal Groups

Definable Compactness and Definable Subgroups of o-Minimal Groups

1999 ◽  
Vol 59 (3) ◽  
pp. 769-786 ◽  
Author(s):  
Ya'acov Peterzil ◽  
Charles Steinhorn
Keyword(s):  
Minimal Groups

Fields of finite Morley rank

2001 ◽  
Vol 66 (2) ◽  
pp. 703-706 ◽  
Author(s):  
Frank Wagner
Keyword(s):  
Algebraic Closure ◽  
Prime Model ◽  
Morley Rank ◽  
Finite Morley Rank ◽  
Minimal Groups

AbstractIf K is a field of finite Morley rank, then for any parameter set A ⊆ Keq the prime model over A is equal to the model-theoretic algebraic closure of A. A field of finite Morley rank eliminates imaginaries. Simlar results hold for minimal groups of finite Morley rank with infinite acl(∅).

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