ABSTRACT
The existence of an infinite simple boundedly generated 2-generated group and the existence of a boundedly simple 2-generated group containing a free noncyclic subgroup are proved.
ACKNOWLEDGMENT
The author would like to thank Alexander Ol'shanskii for suggesting the problems and a possible approach to their solution.
This work was supported in part by the NSF grant DMS 0072307 of Alexander Ol'shanskii and Mark Sapir.
Notes
#Communicated by Alexander Olshanskii.