A January 2005 invitation to random groups
Yann Ollivier
Abstract. Random groups provide a rigorous way to tackle such ques-
tions as "What does a typical (finitely generated) group look like?" or
"What is the behavior of an element of a group when nothing particular
happens?"
We review the results obtained on random groups as of January 2005.
We give proper definitions and list known properties of typical groups. We
also emphasize properties of random elements in a given group. In addition
we present more specific, randomly twisted group constructions providing
new, "wild" examples of groups.
A comprehensive discussion of open problems and perspectives is in-
cluded.
tions as "What does a typical (finitely generated) group look like?" or
"What is the behavior of an element of a group when nothing particular
happens?"
We review the results obtained on random groups as of January 2005.
We give proper definitions and list known properties of typical groups. We
also emphasize properties of random elements in a given group. In addition
we present more specific, randomly twisted group constructions providing
new, "wild" examples of groups.
A comprehensive discussion of open problems and perspectives is in-
cluded.
Anno:
2005
Casa editrice:
Sociedade Brasileira de Matemática
Lingua:
english
Pagine:
100
Collana:
Ensaios Matemáticos 10
File:
DJVU, 6.00 MB
IPFS:
,
english, 2005
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