The Baumslag–Gersten group G was originally introduced in a 1969 paper of Gilbert Baumslag,[1] as an example of a non-residually finite one-relator group with an additional remarkable property that all finite quotient groups of this group are cyclic.
Later, in 1992, Stephen Gersten[2] showed that G, despite being a one-relator group given by a rather simple presentation, has the Dehn function growing very quickly, namely faster than any fixed iterate of the exponential function.
This example remains the fastest known growth of the Dehn function among one-relator groups.
In 2011 Alexei Myasnikov, Alexander Ushakov, and Dong Wook Won[3] proved that G has the word problem solvable in polynomial time.
with stable letter t and two cyclic associated subgroups
: and generalized many of Baumslag's original results in that context.