The Geometry of Finitely Presented Infinite Simple Groups

1992 ◽  
pp. 121-136 ◽  
Author(s):  
Kenneth S. Brown
Keyword(s):  
Simple Groups ◽  
Finitely Presented

scholarly journals Constructing Finitely Presented Simple Groups That Contain Grigorchuk Groups

1999 ◽  
Vol 220 (1) ◽  
pp. 284-313 ◽  
Author(s):  
Claas E. Röver
Keyword(s):  
Simple Groups ◽  
Finitely Presented

scholarly journals THE GROUPS OF RICHARD THOMPSON AND COMPLEXITY

2004 ◽  
Vol 14 (05n06) ◽  
pp. 569-626 ◽  
Author(s):  
JEAN-CAMILLE BIRGET
Keyword(s):  
Word Problem ◽  
Simple Groups ◽  
Direct Products ◽  
Turing Machines ◽  
Group V ◽  
Dehn Functions ◽  
Finitely Presented Groups ◽  
Distortion Functions ◽  
The 1960S ◽  
Finitely Presented

We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We give a faithful representation in the Cuntz C⋆-algebra. For the finitely presented simple group V we show that the word-length and the table size satisfy an n log n relation. We show that the word problem of V belongs to the parallel complexity class AC1 (a subclass of P), whereas the generalized word problem of V is undecidable. We study the distortion functions of V and show that V contains all finite direct products of finitely generated free groups as subgroups with linear distortion. As a consequence, up to polynomial equivalence of functions, the following three sets are the same: the set of distortions of V, the set of Dehn functions of finitely presented groups, and the set of time complexity functions of nondeterministic Turing machines.

Constructing finitely presented infinite nearly simple groups

1994 ◽  
Vol 22 (11) ◽  
pp. 4561-4589 ◽  
Author(s):  
Meenaxi Bhattacharjee
Keyword(s):  
Simple Groups ◽  
Finitely Presented

scholarly journals A diameter bound for finite simple groups of large rank

2017 ◽  
Vol 95 (2) ◽  
pp. 455-474 ◽  
Author(s):  
Arindam Biswas ◽  
Yilong Yang
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Large Rank

scholarly journals Simple groups of birational transformations in dimension two

2020 ◽  
Vol 95 (2) ◽  
pp. 211-246 ◽  
Author(s):  
Christian Urech
Keyword(s):  
Simple Groups ◽  
Birational Transformations
Sign in / Sign up

Export Citation Format

Share Document