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Questions about the branch of algebra that deals with groups.

3 votes
0 answers
121 views

The group $G=\langle t,a \mid t^4=1, (t^{-1}at)^{-1} a (t^{-1} at)=a^2 \rangle$ is non-resid...

A group $G= \langle t,a,| t^4=1, (t^{-1}at)^{-1} a (t^{-1}a t)= a^2 \rangle$ ( I do not remember the reference) was shown as a non -residually finite group. I do not know how to prove it. I will be t …
Kalye's user avatar
  • 81
1 vote
0 answers
138 views

The free products of finitely many finitely generated groups are hyperbolic relative to the fa...

Are there any references how to show that:the free products of finitely many finitely generated groups are hyperbolic relative to the free factors. More precisely, how to show that $G = A \ast B $ is hy …
Kalye's user avatar
  • 81
4 votes
1 answer
194 views

Estimating an upper bound of hyperbolicity constants in Gromov-hyperbolic groups

Is there any good references with an explicit estimating hyperbolicity constants of hyperbolic groups? I was thinking about whether there is any relation between the relator of maximal length in the …
Kalye's user avatar
  • 81