[GAP Forum] Defining New operation from the given group operation

[Vivek Jain]

Dear All,

Suppose that $G$ is a free group of rank 3.
For $a,b$ in  $G$, we define a word $w(a,b):=a^2b^3$. 

If for  $a,b$ in $G$, we define a new binary operation "o" as $aob:=w(a,b)$, then 

is it possible to check the associativity/identity/inverse/commutativity of the new operation using GAP?

with regards

Vivek


 
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Vivek Kumar Jain
Central University of Bihar
Patna, India