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Results tagged with gr.group-theory
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user 81860
Questions about the branch of algebra that deals with groups.
8
votes
Normal subgroups of an extension of the Higman group
The answer to part (a) of your question is that the normal closure of $a^{k_1}\cdot t\cdot a^{k_2} \cdot t \cdot a^{k_3}$ is always equal to the normal closure of $a$ and $t^2$.
This is because the qu …
- 171
4
votes
Normal subgroups of an extension of the Higman group
The answer to part (b) is that the normal closure of the word given in part
(b) is always equal to $G$.
To see this, consider the quotient of $G$ by adding in this case a relation $a^{k}ta^{l}ta^{m}t …
- 171
0
votes
Normal subgroups of an extension of the Higman group
Let me try to answer the first query mentioned in part (c).
Let $G=<a,t|bab^{-1}=a^{2},b=tat^{-1},t^{4}=1>$ and $H=<a,b,c,d|bab^{-1}=a^{2},cbc^{-1}=c^{2},dcd^{-1}=c^{2},ada^{-1}=d^{2}>$
the Higman gr …
- 171